{"id":544173,"date":"2021-10-01T04:23:47","date_gmt":"2021-10-01T04:23:47","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=544173"},"modified":"2021-10-02T04:12:01","modified_gmt":"2021-10-02T04:12:01","slug":"rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/","title":{"rendered":"RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives"},"content":{"rendered":"\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">Class 11: Maths Chapter 30 solutions. Complete Class 11 Maths Chapter 30 Notes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\">RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives<\/h2>\n\n\n\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">RD Sharma 11th Maths Chapter 30, Class 11 Maths Chapter 30 solutions<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">EXERCISE 30.1 PAGE NO: 30.3<\/h4>\n\n\n\n<p><strong>1. Find the derivative of f(x) = 3x at x = 2<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f(x) = 3x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"517\" height=\"318\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-1.png\" alt=\"\" class=\"wp-image-544177\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-1.png 517w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-1-300x185.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-1-400x246.png 400w\" sizes=\"auto, (max-width: 517px) 100vw, 517px\" \/><\/figure>\n\n\n\n<p><strong>2. Find the derivative of f(x) = x<sup>2<\/sup>&nbsp;\u2013 2 at x = 10<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f(x) = x<sup>2<\/sup>&nbsp;\u2013 2<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"519\" height=\"197\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-2.png\" alt=\"\" class=\"wp-image-544178\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-2.png 519w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-2-300x114.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-2-400x152.png 400w\" sizes=\"auto, (max-width: 519px) 100vw, 519px\" \/><\/figure>\n\n\n\n<p>= 0 + 20 = 20<\/p>\n\n\n\n<p>Hence,<\/p>\n\n\n\n<p>Derivative of f(x) = x<sup>2<\/sup>&nbsp;\u2013 2 at x = 10 is 20<\/p>\n\n\n\n<p><strong>3. Find the derivative of f(x) = 99x at x = 100.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f(x) = 99x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"547\" height=\"265\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-3.png\" alt=\"\" class=\"wp-image-544179\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-3.png 547w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-3-300x145.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-3-400x194.png 400w\" sizes=\"auto, (max-width: 547px) 100vw, 547px\" \/><\/figure>\n\n\n\n<p><strong>4. Find the derivative of f(x) = x at x = 1<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f(x) = x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"265\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-4.png\" alt=\"\" class=\"wp-image-544180\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-4.png 548w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-4-300x145.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-4-400x193.png 400w\" sizes=\"auto, (max-width: 548px) 100vw, 548px\" \/><\/figure>\n\n\n\n<p><strong>5. Find the derivative of f(x) = cos x at x = 0<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f(x) = cos x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"590\" height=\"448\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-5.png\" alt=\"\" class=\"wp-image-544181\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-5.png 590w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-5-300x228.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-5-400x304.png 400w\" sizes=\"auto, (max-width: 590px) 100vw, 590px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"182\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-6.png\" alt=\"\" class=\"wp-image-544182\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-6.png 308w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-6-300x177.png 300w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure>\n\n\n\n<p><strong>6. Find the derivative of f(x) = tan x at x = 0<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f(x) = tan x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"514\" height=\"280\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-7.png\" alt=\"\" class=\"wp-image-544183\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-7.png 514w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-7-300x163.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-7-400x218.png 400w\" sizes=\"auto, (max-width: 514px) 100vw, 514px\" \/><\/figure>\n\n\n\n<p><strong>7. Find the derivatives of the following functions at the indicated points:<br>(i) sin x at x = \u03c0\/2<br>(ii) x at x = 1<\/strong><\/p>\n\n\n\n<p><strong>(iii) 2 cos x at x = \u03c0\/2<\/strong><\/p>\n\n\n\n<p><strong>(iv) sin 2xat x = \u03c0\/2<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>(i) sin x at x = \u03c0\/2<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = sin x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"514\" height=\"224\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-8.png\" alt=\"\" class=\"wp-image-544184\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-8.png 514w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-8-300x131.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-8-400x174.png 400w\" sizes=\"auto, (max-width: 514px) 100vw, 514px\" \/><\/figure>\n\n\n\n<p>[Since it is of indeterminate form. Let us try to evaluate the limit.]<\/p>\n\n\n\n<p>We know that 1 \u2013 cos x = 2 sin<sup>2<\/sup>(x\/2)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"592\" height=\"380\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-9.png\" alt=\"\" class=\"wp-image-544185\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-9.png 592w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-9-300x193.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-9-400x257.png 400w\" sizes=\"auto, (max-width: 592px) 100vw, 592px\" \/><\/figure>\n\n\n\n<p><strong>(ii) x at x = 1<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"265\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-10.png\" alt=\"\" class=\"wp-image-544186\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-10.png 548w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-10-300x145.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-10-400x193.png 400w\" sizes=\"auto, (max-width: 548px) 100vw, 548px\" \/><\/figure>\n\n\n\n<p><strong>(iii) 2 cos x at x = \u03c0\/2<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = 2 cos x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"511\" height=\"352\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-11.png\" alt=\"\" class=\"wp-image-544187\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-11.png 511w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-11-300x207.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-11-400x276.png 400w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/figure>\n\n\n\n<p><strong>(iv) sin 2xat x = \u03c0\/2<\/strong><\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = sin 2x<\/p>\n\n\n\n<p>By using the derivative formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"511\" height=\"294\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-12.png\" alt=\"\" class=\"wp-image-544188\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-12.png 511w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-12-300x173.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-12-400x230.png 400w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/figure>\n\n\n\n<p>[Since it is of indeterminate form. We shall apply sandwich theorem to evaluate the limit.]<\/p>\n\n\n\n<p>Now, multiply numerator and denominator by 2, we get<\/p>\n\n\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">EXERCISE 30.2 PAGE NO: 30.25<\/h4>\n\n\n\n<p><strong>1. Differentiate each of the following from first principles:<br>(i) 2\/x<br>(ii) 1\/\u221ax<\/strong><\/p>\n\n\n\n<p><strong>(iii) 1\/x<sup>3<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(iv) [x<sup>2<\/sup>&nbsp;+ 1]\/ x<\/strong><\/p>\n\n\n\n<p><strong>(v) [x<sup>2<\/sup>&nbsp;\u2013 1] \/ x<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>(i)&nbsp;<\/strong>2\/x<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = 2\/x<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"405\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-14.png\" alt=\"\" class=\"wp-image-544189\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-14.png 347w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-14-257x300.png 257w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/figure>\n\n\n\n<p>\u2234 Derivative of f(x) = 2\/x is -2x<sup>-2<\/sup><\/p>\n\n\n\n<p><strong>(ii)&nbsp;<\/strong>1\/\u221ax<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = 1\/\u221ax<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"482\" height=\"440\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-15.png\" alt=\"\" class=\"wp-image-544190\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-15.png 482w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-15-300x274.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-15-400x365.png 400w\" sizes=\"auto, (max-width: 482px) 100vw, 482px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"220\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-16.png\" alt=\"\" class=\"wp-image-544191\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p>\u2234 Derivative of f(x) = 1\/\u221ax is -1\/2 x<sup>-3\/2<\/sup><\/p>\n\n\n\n<p><strong>(iii) 1\/x<sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = 1\/x<sup>3<\/sup><\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"413\" height=\"468\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-17.png\" alt=\"\" class=\"wp-image-544192\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-17.png 413w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-17-265x300.png 265w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-17-400x453.png 400w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"154\" height=\"163\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-18.png\" alt=\"\" class=\"wp-image-544193\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p>\u2234 Derivative of f(x) = 1\/x<sup>3<\/sup>&nbsp;is -3x<sup>-4<\/sup><\/p>\n\n\n\n<p><strong>(iv)&nbsp;<\/strong>[x<sup>2<\/sup>&nbsp;+ 1]\/ x<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = [x<sup>2<\/sup>&nbsp;+ 1]\/ x<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"337\" height=\"75\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-19.png\" alt=\"\" class=\"wp-image-544194\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-19.png 337w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-19-300x67.png 300w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"552\" height=\"518\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-20.png\" alt=\"\" class=\"wp-image-544195\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-20.png 552w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-20-300x282.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-20-400x375.png 400w\" sizes=\"auto, (max-width: 552px) 100vw, 552px\" \/><\/figure>\n\n\n\n<p>= 1 \u2013 1\/x<sup>2<\/sup><\/p>\n\n\n\n<p>\u2234 Derivative of f(x) =&nbsp;1 \u2013 1\/x<sup>2<\/sup><\/p>\n\n\n\n<p><strong>(v)&nbsp;<\/strong>[x<sup>2<\/sup>&nbsp;\u2013 1] \/ x<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = [x<sup>2<\/sup>&nbsp;\u2013 1]\/ x<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"168\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-21.png\" alt=\"\" class=\"wp-image-544197\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-21.png 345w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-21-300x146.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"546\" height=\"448\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-22.png\" alt=\"\" class=\"wp-image-544196\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-22.png 546w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-22-300x246.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-22-400x328.png 400w\" sizes=\"auto, (max-width: 546px) 100vw, 546px\" \/><\/figure>\n\n\n\n<p><strong>2. Differentiate each of the following from first principles:<\/strong><\/p>\n\n\n\n<p><strong>(i) e<sup>-x<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(ii) e<sup>3x<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(iii) e<sup>ax+b<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>(i)&nbsp;<\/strong>e<sup>-x<\/sup><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = e<sup>-x<\/sup><\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"339\" height=\"142\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-23.png\" alt=\"\" class=\"wp-image-544198\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-23.png 339w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-23-300x126.png 300w\" sizes=\"auto, (max-width: 339px) 100vw, 339px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"328\" height=\"390\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-24.png\" alt=\"\" class=\"wp-image-544199\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-24.png 328w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-24-252x300.png 252w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/figure>\n\n\n\n<p><strong>(ii)&nbsp;<\/strong>e<sup>3x<\/sup><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = e<sup>3x<\/sup><\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"333\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-25.png\" alt=\"\" class=\"wp-image-544200\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-25.png 344w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-25-300x290.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"449\" height=\"252\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-26.png\" alt=\"\" class=\"wp-image-544201\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-26.png 449w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-26-300x168.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-26-400x224.png 400w\" sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/><\/figure>\n\n\n\n<p><strong>(iii)&nbsp;<\/strong>e<sup>ax+b<\/sup><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = e<sup>ax+b<\/sup><\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"446\" height=\"454\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-27.png\" alt=\"\" class=\"wp-image-544202\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-27.png 446w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-27-295x300.png 295w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-27-400x407.png 400w\" sizes=\"auto, (max-width: 446px) 100vw, 446px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"305\" height=\"150\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-28.png\" alt=\"\" class=\"wp-image-544203\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-28.png 305w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-28-300x148.png 300w\" sizes=\"auto, (max-width: 305px) 100vw, 305px\" \/><\/figure>\n\n\n\n<p><strong>3.<\/strong>&nbsp;<strong>Differentiate each of the following from first principles:<\/strong><\/p>\n\n\n\n<p><strong>(i) \u221a(sin 2x)<\/strong><\/p>\n\n\n\n<p><strong>(ii) sin x\/x<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>(i)&nbsp;<\/strong>\u221a(sin 2x)<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = \u221a(sin 2x)<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"612\" height=\"426\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-29.png\" alt=\"\" class=\"wp-image-544204\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-29.png 612w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-29-300x209.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-29-400x278.png 400w\" sizes=\"auto, (max-width: 612px) 100vw, 612px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"617\" height=\"462\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-30.png\" alt=\"\" class=\"wp-image-544205\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-30.png 617w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-30-300x225.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-30-400x300.png 400w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-30-200x150.png 200w\" sizes=\"auto, (max-width: 617px) 100vw, 617px\" \/><\/figure>\n\n\n\n<p><strong>(ii)&nbsp;<\/strong>sin x\/x<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = sin x\/x<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"228\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-31.png\" alt=\"\" class=\"wp-image-544206\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-31.png 347w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-31-300x197.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"639\" height=\"429\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-32.png\" alt=\"\" class=\"wp-image-544207\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-32.png 639w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-32-300x201.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-32-400x269.png 400w\" sizes=\"auto, (max-width: 639px) 100vw, 639px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"367\" height=\"230\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-33.png\" alt=\"\" class=\"wp-image-544208\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-33.png 367w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-33-300x188.png 300w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/><\/figure>\n\n\n\n<p><strong>4. Differentiate the following from first principles:<\/strong><\/p>\n\n\n\n<p><strong>(i) tan<sup>2<\/sup>&nbsp;x<\/strong><\/p>\n\n\n\n<p><strong>(ii) tan (2x + 1)<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>(i)&nbsp;<\/strong>tan<sup>2<\/sup>&nbsp;x<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = tan<sup>2<\/sup>&nbsp;x<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"451\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-34.png\" alt=\"\" class=\"wp-image-544209\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-34.png 640w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-34-300x211.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-34-400x282.png 400w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"509\" height=\"328\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-35.png\" alt=\"\" class=\"wp-image-544210\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-35.png 509w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-35-300x193.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-35-400x258.png 400w\" sizes=\"auto, (max-width: 509px) 100vw, 509px\" \/><\/figure>\n\n\n\n<p><strong>(ii)&nbsp;<\/strong>tan (2x + 1)<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = tan (2x + 1)<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"637\" height=\"449\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-36.png\" alt=\"\" class=\"wp-image-544211\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-36.png 637w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-36-300x211.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-36-400x282.png 400w\" sizes=\"auto, (max-width: 637px) 100vw, 637px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"351\" height=\"187\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-37.png\" alt=\"\" class=\"wp-image-544212\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-37.png 351w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-37-300x160.png 300w\" sizes=\"auto, (max-width: 351px) 100vw, 351px\" \/><\/figure>\n\n\n\n<p><strong>5. Differentiate the following from first principles:<\/strong><\/p>\n\n\n\n<p><strong>(i) sin \u221a2x<\/strong><\/p>\n\n\n\n<p><strong>(ii) cos \u221ax<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>(i)&nbsp;<\/strong>sin \u221a2x<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = sin \u221a2x<\/p>\n\n\n\n<p>f (x + h) = sin \u221a2(x+h)<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"561\" height=\"478\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-38.png\" alt=\"\" class=\"wp-image-544213\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-38.png 561w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-38-300x256.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-38-400x341.png 400w\" sizes=\"auto, (max-width: 561px) 100vw, 561px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"275\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-39.png\" alt=\"\" class=\"wp-image-544214\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-39.png 384w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-39-300x215.png 300w\" sizes=\"auto, (max-width: 384px) 100vw, 384px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"72\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-40.png\" alt=\"\" class=\"wp-image-544215\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p><strong>(ii)&nbsp;<\/strong>cos \u221ax<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = cos \u221ax<\/p>\n\n\n\n<p>f (x + h) = cos \u221a(x+h)<\/p>\n\n\n\n<p>By using the formula,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"541\" height=\"490\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-41.png\" alt=\"\" class=\"wp-image-544216\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-41.png 541w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-41-300x272.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-41-400x362.png 400w\" sizes=\"auto, (max-width: 541px) 100vw, 541px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"352\" height=\"124\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-42.png\" alt=\"\" class=\"wp-image-544217\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-42.png 352w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-42-300x106.png 300w\" sizes=\"auto, (max-width: 352px) 100vw, 352px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"353\" height=\"162\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-43.png\" alt=\"\" class=\"wp-image-544218\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-43.png 353w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-43-300x138.png 300w\" sizes=\"auto, (max-width: 353px) 100vw, 353px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">EXERCISE 30.3 PAGE NO: 30.33<\/h4>\n\n\n\n<p><strong>Differentiate the following with respect to x:<\/strong><\/p>\n\n\n\n<p><strong>1. x<sup>4<\/sup>&nbsp;\u2013 2sin x + 3 cos x<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = x<sup>4<\/sup>&nbsp;\u2013 2sin x + 3 cos x<\/p>\n\n\n\n<p>Differentiate on both the sides with respect to x, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"336\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-44.png\" alt=\"\" class=\"wp-image-544219\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-44.png 345w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-44-300x292.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><\/figure>\n\n\n\n<p><strong>2.<\/strong>&nbsp;<strong>3<sup>x<\/sup>&nbsp;+ x<sup>3<\/sup>&nbsp;+ 3<sup>3<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = 3<sup>x<\/sup>&nbsp;+ x<sup>3<\/sup>&nbsp;+ 3<sup>3<\/sup><\/p>\n\n\n\n<p>Differentiate on both the sides with respect to x, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"264\" height=\"157\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-45.png\" alt=\"\" class=\"wp-image-544220\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"167\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-46.png\" alt=\"\" class=\"wp-image-544221\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"157\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-47.gif\" alt=\"\" class=\"wp-image-544222\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-48.gif\" alt=\"\" class=\"wp-image-544223\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p>Differentiate on both the sides with respect to x, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"321\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-49.png\" alt=\"\" class=\"wp-image-544224\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-49.png 345w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-49-300x279.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><\/figure>\n\n\n\n<p><strong>4. e<sup>x log a<\/sup>&nbsp;+ e<sup>a log x<\/sup>&nbsp;+ e<sup>a log a<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = e<sup>x log a<\/sup>&nbsp;+ e<sup>a log x<\/sup>&nbsp;+ e<sup>a log a<\/sup><\/p>\n\n\n\n<p>We know that,<\/p>\n\n\n\n<p>e<sup>log f(x)<\/sup>&nbsp;=&nbsp;f(x)<\/p>\n\n\n\n<p>So,<\/p>\n\n\n\n<p>f(x) = a<sup>x<\/sup>&nbsp;+ x<sup>a<\/sup>&nbsp;+ a<sup>a<\/sup><\/p>\n\n\n\n<p>Differentiate on both the sides with respect to x, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"299\" height=\"310\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-50.png\" alt=\"\" class=\"wp-image-544225\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-50.png 299w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-50-289x300.png 289w\" sizes=\"auto, (max-width: 299px) 100vw, 299px\" \/><\/figure>\n\n\n\n<p><strong>5. (2x<sup>2<\/sup>&nbsp;+ 1) (3x + 2)<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<p>f (x) = (2x<sup>2<\/sup>&nbsp;+ 1) (3x + 2)<\/p>\n\n\n\n<p>= 6x<sup>3<\/sup>&nbsp;+ 4x<sup>2<\/sup>&nbsp;+ 3x + 2<\/p>\n\n\n\n<p>Differentiate on both the sides with respect to x, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"367\" height=\"296\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-51.png\" alt=\"\" class=\"wp-image-544226\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-51.png 367w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-51-300x242.png 300w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">EXERCISE 30.4 PAGE NO: 30.39<\/h4>\n\n\n\n<p><strong>Differentiate the following functions with respect to x:<\/strong><\/p>\n\n\n\n<p><strong>1. x<sup>3<\/sup>&nbsp;sin x<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider y = x<sup>3<\/sup>&nbsp;sin x<\/p>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a product of two functions say u and v where,<\/p>\n\n\n\n<p>u = x<sup>3<\/sup>&nbsp;and v = sin x<\/p>\n\n\n\n<p>\u2234&nbsp;y = uv<\/p>\n\n\n\n<p>Now let us apply product rule of differentiation.<\/p>\n\n\n\n<p>By using product rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"533\" height=\"307\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-52.png\" alt=\"\" class=\"wp-image-544227\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-52.png 533w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-52-300x173.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-52-400x230.png 400w\" sizes=\"auto, (max-width: 533px) 100vw, 533px\" \/><\/figure>\n\n\n\n<p><strong>2. x<sup>3<\/sup>&nbsp;e<sup>x<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider y = x<sup>3<\/sup>&nbsp;e<sup>x<\/sup><\/p>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a product of two functions say u and v where,<\/p>\n\n\n\n<p>u = x<sup>3<\/sup>&nbsp;and v = e<sup>x<\/sup><\/p>\n\n\n\n<p>\u2234&nbsp;y = uv<\/p>\n\n\n\n<p>Now let us apply product rule of differentiation.<\/p>\n\n\n\n<p>By using product rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"448\" height=\"311\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-53.png\" alt=\"\" class=\"wp-image-544228\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-53.png 448w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-53-300x208.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-53-400x278.png 400w\" sizes=\"auto, (max-width: 448px) 100vw, 448px\" \/><\/figure>\n\n\n\n<p><strong>3. x<sup>2<\/sup>&nbsp;e<sup>x<\/sup>&nbsp;log x<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider y = x<sup>2<\/sup>&nbsp;e<sup>x<\/sup>&nbsp;log x<\/p>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a product of two functions say u and v where,<\/p>\n\n\n\n<p>u = x<sup>2<\/sup>&nbsp;and v = e<sup>x<\/sup><\/p>\n\n\n\n<p>\u2234&nbsp;y = uv<\/p>\n\n\n\n<p>Now let us apply product rule of differentiation.<\/p>\n\n\n\n<p>By using product rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"473\" height=\"278\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-54.png\" alt=\"\" class=\"wp-image-544229\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-54.png 473w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-54-300x176.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-54-400x235.png 400w\" sizes=\"auto, (max-width: 473px) 100vw, 473px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"503\" height=\"87\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-55.png\" alt=\"\" class=\"wp-image-544230\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-55.png 503w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-55-300x52.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-55-400x69.png 400w\" sizes=\"auto, (max-width: 503px) 100vw, 503px\" \/><\/figure>\n\n\n\n<p><strong>4. x<sup>n<\/sup>&nbsp;tan x<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider y = x<sup>n<\/sup>&nbsp;tan x<\/p>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a product of two functions say u and v where,<\/p>\n\n\n\n<p>u = x<sup>n<\/sup>&nbsp;and v = tan x<\/p>\n\n\n\n<p>\u2234&nbsp;y = uv<\/p>\n\n\n\n<p>Now let us apply product rule of differentiation.<\/p>\n\n\n\n<p>By using product rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"538\" height=\"324\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-56.png\" alt=\"\" class=\"wp-image-544231\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-56.png 538w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-56-300x181.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-56-400x241.png 400w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/figure>\n\n\n\n<p><strong>5. x<sup>n<\/sup>&nbsp;log<sub>a<\/sub>&nbsp;x<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider y = x<sup>n<\/sup>&nbsp;log<sub>a<\/sub>&nbsp;x<\/p>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a product of two functions say u and v where,<\/p>\n\n\n\n<p>u = x<sup>n<\/sup>&nbsp;and v = log<sub>a<\/sub>&nbsp;x<\/p>\n\n\n\n<p>\u2234&nbsp;y = uv<\/p>\n\n\n\n<p>Now let us apply product rule of differentiation.<\/p>\n\n\n\n<p>By using product rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"557\" height=\"311\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-57.png\" alt=\"\" class=\"wp-image-544232\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-57.png 557w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-57-300x168.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-57-400x223.png 400w\" sizes=\"auto, (max-width: 557px) 100vw, 557px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">EXERCISE 30.5 PAGE NO: 30.44<\/h4>\n\n\n\n<p><strong>Differentiate the following functions with respect to x:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"73\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-58.gif\" alt=\"\" class=\"wp-image-544233\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider<\/p>\n\n\n\n<p>y =<br><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"49\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-59.gif\" alt=\"\" class=\"wp-image-544234\"\/><\/figure>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a fraction of two functions say u and v where,<\/p>\n\n\n\n<p>u = x<sup>2<\/sup>&nbsp;+ 1&nbsp;and v = x + 1<\/p>\n\n\n\n<p>\u2234&nbsp;y = u\/v<\/p>\n\n\n\n<p>Now let us apply quotient rule of differentiation.<\/p>\n\n\n\n<p>By using quotient rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"515\" height=\"407\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-60.png\" alt=\"\" class=\"wp-image-544235\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-60.png 515w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-60-300x237.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-60-400x316.png 400w\" sizes=\"auto, (max-width: 515px) 100vw, 515px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"76\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-61.gif\" alt=\"\" class=\"wp-image-544236\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider<\/p>\n\n\n\n<p>y =<br><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"51\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-62.gif\" alt=\"\" class=\"wp-image-544237\"\/><\/figure>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a fraction of two functions say u and v where,<\/p>\n\n\n\n<p>u = 2x \u2013 1&nbsp;and v = x<sup>2<\/sup>&nbsp;+ 1<\/p>\n\n\n\n<p>\u2234&nbsp;y = u\/v<\/p>\n\n\n\n<p>Now let us apply quotient rule of differentiation.<\/p>\n\n\n\n<p>By using quotient rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"526\" height=\"418\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-63.png\" alt=\"\" class=\"wp-image-544238\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-63.png 526w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-63-300x238.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-63-400x318.png 400w\" sizes=\"auto, (max-width: 526px) 100vw, 526px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"97\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-64.gif\" alt=\"\" class=\"wp-image-544239\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider<\/p>\n\n\n\n<p>y =<br><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"68\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-65.gif\" alt=\"\" class=\"wp-image-544240\"\/><\/figure>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a fraction of two functions say u and v where,<\/p>\n\n\n\n<p>u = x + e<sup>x<\/sup>&nbsp;and v = 1 + log x<\/p>\n\n\n\n<p>\u2234&nbsp;y = u\/v<\/p>\n\n\n\n<p>Now let us apply quotient rule of differentiation.<\/p>\n\n\n\n<p>By using quotient rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"459\" height=\"480\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-66.png\" alt=\"\" class=\"wp-image-544241\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-66.png 459w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-66-287x300.png 287w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-66-400x418.png 400w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"96\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-67.png\" alt=\"\" class=\"wp-image-544242\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"111\" height=\"40\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-68.gif\" alt=\"\" class=\"wp-image-544243\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider<\/p>\n\n\n\n<p>y =<br><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"78\" height=\"37\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-69.gif\" alt=\"\" class=\"wp-image-544244\"\/><\/figure>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a fraction of two functions say u and v where,<\/p>\n\n\n\n<p>u = e<sup>x<\/sup>&nbsp;\u2013 tan x&nbsp;and v = cot x \u2013 x<sup>n<\/sup><\/p>\n\n\n\n<p>\u2234&nbsp;y = u\/v<\/p>\n\n\n\n<p>Now let us apply quotient rule of differentiation.<\/p>\n\n\n\n<p>By using quotient rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"464\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-70.png\" alt=\"\" class=\"wp-image-544245\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-70.png 606w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-70-300x230.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-70-400x306.png 400w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"132\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-71.gif\" alt=\"\" class=\"wp-image-544246\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let us consider<\/p>\n\n\n\n<p>y =<br><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"98\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-72.gif\" alt=\"\" class=\"wp-image-544247\"\/><\/figure>\n\n\n\n<p>We need to find dy\/dx<\/p>\n\n\n\n<p>We know that y is a fraction of two functions say u and v where,<\/p>\n\n\n\n<p>u = ax<sup>2<\/sup>&nbsp;+ bx + c&nbsp;and v = px<sup>2<\/sup>&nbsp;+ qx + r<\/p>\n\n\n\n<p>\u2234&nbsp;y = u\/v<\/p>\n\n\n\n<p>Now let us apply quotient rule of differentiation.<\/p>\n\n\n\n<p>By using quotient rule, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"547\" height=\"448\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-73.png\" alt=\"\" class=\"wp-image-544248\" title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-73.png 547w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-73-300x246.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-73-400x328.png 400w\" sizes=\"auto, (max-width: 547px) 100vw, 547px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-11-maths-chapter-30-download-pdf\">RD Sharma Solutions for Class 11 Maths Chapter 30:&nbsp;<strong>Download PDF<\/strong><\/h2>\n\n\n\n<p>RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives<\/p>\n\n\n\n<p><a href=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/RD-Sharma-Solutions-for-Class-11-Maths-Chapter-30\u2013Derivatives.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download PDF<\/strong>: RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives PDF<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Chapterwise RD Sharma Solutions for Class 11&nbsp;Maths :<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-1-sets\/\">Chapter 1\u2013Sets<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-2-relations\/\">Chapter 2\u2013Relations<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-3-functions\/\">Chapter 3\u2013Functions<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-4-measurement-of-angles\/\">Chapter 4\u2013Measurement of Angles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-5-trigonometric-functions\/\">Chapter 5\u2013Trigonometric Functions<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-6-graphs-of-trigonometric-functions\/\">Chapter 6\u2013Graphs of Trigonometric Functions<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-7-values-of-trigonometric-functions-at-sum-or-difference-of-angles\/\">Chapter 7\u2013Values of Trigonometric Functions at Sum or Difference of Angles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-8-transformation-formulae\/\">Chapter 8\u2013Transformation Formulae<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-9-values-of-trigonometric-functions-at-multiples-and-submultiples-of-an-angle\/\">Chapter 9\u2013Values of Trigonometric Functions at Multiples and Submultiples of an Angle<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-10-sine-and-cosine-formulae-and-their-applications\/\">Chapter 10\u2013Sine and Cosine Formulae and their Applications<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-11-trigonometric-equations\/\">Chapter 11\u2013Trigonometric Equations<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-12-mathematical-induction\/\">Chapter 12\u2013Mathematical Induction<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-13-complex-numbers\/\">Chapter 13\u2013Complex Numbers<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-14-quadratic-equations\/\">Chapter 14\u2013Quadratic Equations<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-15-linear-inequations\/\">Chapter 15\u2013Linear Inequations<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-16-permutations\/\">Chapter 16\u2013Permutations<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-17-combinations\/\">Chapter 17\u2013Combinations<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-18-binomial-theorem\/\">Chapter 18\u2013Binomial Theorem<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-19-arithmetic-progressions\/\">Chapter 19\u2013Arithmetic Progressions<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-20-geometric-progressions\/\">Chapter 20\u2013Geometric Progressions<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-21-some-special-series\/\">Chapter 21\u2013Some Special Series<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-22-brief-review-of-cartesian-system-of-rectangular-coordinates\/\">Chapter 22\u2013Brief review of Cartesian System of Rectangular Coordinates<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-23-the-straight-lines\/\">Chapter 23\u2013The Straight Lines<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-24-the-circle\/\">Chapter 24\u2013The Circle<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-25-parabola\/\">Chapter 25\u2013Parabola<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-26-ellipse\/\">Chapter 26\u2013Ellipse<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-27-hyperbola\/\">Chapter 27\u2013Hyperbola<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-28-introduction-to-three-dimensional-coordinate-geometry\/\">Chapter 28\u2013Introduction to Three Dimensional Coordinate Geometry<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-29-limits\/\">Chapter 29\u2013Limits<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/\">Chapter 30\u2013Derivatives<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-31-mathematical-reasoning\/\">Chapter 31\u2013Mathematical Reasoning<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-32-statistics\/\">Chapter 32\u2013Statistics<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-33-probability\/\">Chapter 33\u2013Probability<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">About RD Sharma<\/h2>\n\n\n\n<p>RD Sharma i<em>sn&#8217;t the kind of author you&#8217;d bump into at lit fests. But his bestselling books have helped many&nbsp;<\/em>CBSE<em>&nbsp;students lose their dread of&nbsp;<\/em>maths<em>. Sunday Times profiles the tutor turned internet star<\/em><br>He dreams of algorithms that would give most people nightmares. And, spends every waking hour thinking of ways to explain concepts like &#8216;series solution of linear differential equations&#8217;. Meet Dr&nbsp;Ravi Dutt Sharma&nbsp;\u2014&nbsp;mathematics&nbsp;teacher and author of 25 reference books \u2014 whose name evokes as much awe as the subject he teaches. And though students have used his thick tomes for the last 31 years to ace the dreaded maths exam, it&#8217;s only recently that a spoof video turned the tutor into a YouTube star.<\/p>\n\n\n\n<p>R D Sharma had a good laugh but said he shared little with his on-screen persona except for the love for maths. &#8220;I like to spend all my time thinking and writing about maths problems. I find it relaxing,&#8221; he says. When he is not writing books explaining mathematical concepts for classes 6 to 12 and engineering students, Sharma is busy dispensing his duty as vice-principal and head of department of science and humanities at Delhi government&#8217;s Guru Nanak Dev Institute of Technology.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Read More<\/h2>\n\n\n\n<ul class=\"wp-block-yoast-seo-related-links\"><li><a href=\"https:\/\/www.indcareer.com\/schools\/ncert-solutions-for-12th-class-maths-chapter-6-application-of-derivatives\/\">NCERT Solutions for 12th Class Maths: Chapter 6-Application of Derivatives<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ncert-solutions-for-class-10th-maths-chapter-3-pair-of-linear-equations-in-two-variables\/\">NCERT Solutions for Class 10th Maths: Chapter 3 Pair of Linear Equations in Two Variables<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ncert-solutions-for-12th-class-business-studies-chapter-11-marketing\/\">NCERT Solutions for 12th Class Business Studies: Chapter 11- Marketing<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-28-introduction-to-three-dimensional-coordinate-geometry\/\">RD Sharma Solutions for Class 11 Maths Chapter 28\u2013Introduction to Three Dimensional Coordinate Geometry<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-17-increasing-and-decreasing-functions\/\">RD Sharma Solutions for Class 12 Maths Chapter 17\u2013Increasing and Decreasing Functions<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Class 11: Maths Chapter 30 solutions. Complete Class 11 Maths Chapter 30 Notes. RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives RD Sharma 11th Maths Chapter 30, Class 11 Maths Chapter 30 solutions EXERCISE 30.1 PAGE NO: 30.3 1. Find the derivative of f(x) = 3x at x = 2 Solution: Given: f(x) = [&hellip;]<\/p>\n","protected":false},"author":302,"featured_media":544176,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[1411,919],"tags":[1962],"boards":[],"class_list":["post-544173","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book-solutions","category-class-11","tag-rd-sharma-solutions","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.1.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>RD Sharma Solutions for Class 11, maths Chapter 30 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives | Browse all Class 11 Maths Chapters RD Sharma books - IndCareer Schools\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives\" \/>\n<meta property=\"og:description\" content=\"Class 11: Maths Chapter 30 solutions. Complete Class 11 Maths Chapter 30 Notes. RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives RD Sharma\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-01T04:23:47+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-02T04:12:01+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/i2.wp.com\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class11m30.png?fit=1200%2C675&ssl=1\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"675\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"24 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"RD Sharma Solutions for Class 11 Maths Chapter 30\u2013Derivatives\",\"datePublished\":\"2021-10-01T04:23:47+00:00\",\"dateModified\":\"2021-10-02T04:12:01+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/\"},\"wordCount\":1779,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class11m30.png\",\"keywords\":[\"RD Sharma Solutions\"],\"articleSection\":[\"Book Solutions\",\"class 11\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives\/\",\"name\":\"RD Sharma Solutions for Class 11, maths Chapter 30 - 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Complete Class 11 Maths Chapter 30 Notes. 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