{"id":64129,"date":"2023-09-05T18:22:00","date_gmt":"2023-09-05T12:52:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=64129"},"modified":"2023-11-02T10:04:54","modified_gmt":"2023-11-02T04:34:54","slug":"rd-sharma-solutions-class-11-maths-chapter-30-derivatives","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/","title":{"rendered":"RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives (Updated For 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-121250\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-30-Derivatives.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 30\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-30-Derivatives.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-30-Derivatives-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 30<\/strong> &#8211; Derivatives:\u00a0Derivatives are considered to be among the most important chapters of Class 11 mathematics. You will learn to use limits (which you have studied in the previous chapter) with derivatives. This chapter will also help you in your Class 12 Maths exam prep. Therefore, it is important to get clear with the concepts present in this chapter. Prepare <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 11 Maths<\/a> Chapter 30 for better results.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d20c52c4160\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69d20c52c4160\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#download-rd-sharma-solutions-class-11-maths-chapter-30-%e2%80%93-derivatives-pdf\" title=\"Download RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives PDF\">Download RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#exercise-wise-rd-sharma-solutions-class-11-maths-chapter-30-%e2%80%93-derivatives\" title=\"Exercise-wise RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives\">Exercise-wise RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#rd-sharma-solutions-class-11-maths-chapter-30-exercise-301\" title=\"RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.1\">RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#rd-sharma-solutions-class-11-maths-chapter-30-exercise-302\" title=\"RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.2\">RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#rd-sharma-solutions-class-11-maths-chapter-30-exercise-303\" title=\"RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.3\">RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#rd-sharma-solutions-class-11-maths-chapter-30-exercise-304\" title=\"RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.4\">RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#rd-sharma-solutions-class-11-maths-chapter-30-exercise-305\" title=\"RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.5\">RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.5<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#access-rd-sharma-solutions-class-11-maths-chapter-30\" title=\"Access RD Sharma Solutions Class 11 Maths Chapter 30\">Access RD Sharma Solutions Class 11 Maths Chapter 30<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#exercise-301-page-no-303\" title=\"EXERCISE 30.1 PAGE NO: 30.3\">EXERCISE 30.1 PAGE NO: 30.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#since-it-is-of-indeterminate-form-let-us-try-to-evaluate-the-limit\" title=\"[Since it is of indeterminate form, let us try to evaluate the limit.]\">[Since it is of indeterminate form, let us try to evaluate the limit.]<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#since-it-is-of-indeterminate-form-we-shall-apply-the-sandwich-theorem-to-evaluate-the-limit\" title=\"[Since it is of indeterminate form, we shall apply the sandwich theorem to evaluate the limit.]\">[Since it is of indeterminate form, we shall apply the sandwich theorem to evaluate the limit.]<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#important-topics-from-rd-sharma-solutions-class-11-maths-chapter-30-derivatives\" title=\"Important Topics from RD Sharma Solutions Class 11 Maths Chapter 30- Derivatives\">Important Topics from RD Sharma Solutions Class 11 Maths Chapter 30- Derivatives<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#key-take-away-from-class11-maths-chapter-30-derivatives-rd-sharma-solutions\" title=\"Key Take Away from Class11 Maths Chapter 30- Derivatives RD Sharma Solutions\">Key Take Away from Class11 Maths Chapter 30- Derivatives RD Sharma Solutions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#rd-sharma-solutions-class11-maths-chapter-30\" title=\"RD Sharma Solutions Class11 Maths Chapter 30\">RD Sharma Solutions Class11 Maths Chapter 30<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#faqs-on-rd-sharma-solutions-class-11-maths-chapter-30\" title=\"FAQs on RD Sharma Solutions Class 11 Maths Chapter 30\">FAQs on RD Sharma Solutions Class 11 Maths Chapter 30<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#are-the-solutions-rd-sharma-solutions-class-11-maths-chapter-30-relevant\" title=\"Are the solutions RD Sharma Solutions Class 11 Maths Chapter 30\u00a0relevant?\">Are the solutions RD Sharma Solutions Class 11 Maths Chapter 30\u00a0relevant?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#is-it-even-beneficial-to-study-rd-sharma-solutions-class-11-maths-chapter-30\" title=\"Is it even beneficial to study RD Sharma Solutions Class 11 Maths Chapter 30?\">Is it even beneficial to study RD Sharma Solutions Class 11 Maths Chapter 30?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/#can-i-access-the-rd-sharma-solutions-class-11-maths-chapter-30-pdf-offline\" title=\"Can I access the RD Sharma Solutions Class 11 Maths Chapter 30 PDF offline?\">Can I access the RD Sharma Solutions Class 11 Maths Chapter 30 PDF offline?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-11-maths-chapter-30-%e2%80%93-derivatives-pdf\"><\/span>Download RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/rd-30.pdf\">RD Sharma Solutions Class 11 Maths Chapter 30<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/rd-30.pdf\",\"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"exercise-wise-rd-sharma-solutions-class-11-maths-chapter-30-%e2%80%93-derivatives\"><\/span>Exercise-wise RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<table style=\"width: 99.9129%;\" width=\"591\">\n<tbody>\n<tr>\n<td style=\"width: 765px;\" width=\"296\">\n<p><strong>Exercise Solutions<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 765px;\" width=\"296\">\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-exercise-30-1\/\">RD Sharma Solutions Class 11 Maths Chapter 30 for Exercise 30.1<\/a><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 765px;\" width=\"296\">\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-exercise-30-2\/\">RD Sharma Solutions Class 11 Maths Chapter 30 for Exercise 30.2<\/a><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 765px;\" width=\"296\">\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-exercise-30-3\/\">RD Sharma Solutions Class 11 Maths Chapter 30 for Exercise 30.3<\/a><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 765px;\" width=\"296\">\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-exercise-30-4\/\">RD Sharma Solutions Class 11 Maths Chapter 30 for Exercise 30.4<\/a><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 765px;\" width=\"296\">\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-exercise-30-5\/\">RD Sharma Solutions Class 11 Maths Chapter 30 for Exercise 30.5<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-11-maths-chapter-30-exercise-301\"><\/span><span style=\"font-size: 24px; background-color: initial;\">RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.1<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Exercise 30.1 is all about derivatives at a point. Throughout this chapter, it will be assumed that a given function f(x) is differentiable at every point in its domain i.e. exists for all c in its domain.<\/p>\n<p>In this exercise, you will encounter questions like these, <em>Find the derivative of f(x) = 3x at x=2.<\/em><\/p>\n<p>This exercise is super easy. Once you cross this hurdle of solving basic derivatives you can move ahead with further exercises.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-11-maths-chapter-30-exercise-302\"><\/span>RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Exercise &#8211; 30.2 covers some more important topics of derivatives. It includes finding derivatives of a function, and differentiation from the first principle.<\/p>\n<p>This exercise will add more when you go for other exercises. Go through each question and concept carefully while solving questions of Exercise &#8211; 30.2. RD Sharma solutions will help you understand and solve questions effectively.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-11-maths-chapter-30-exercise-303\"><\/span>RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Every exercise adds up one extra concept and finally mixes all of them to let students know how to proceed when a question comes to test all the concepts together.<\/p>\n<p>Exercise &#8211; 30.3 introduces students to fundamental rules for differentiation. There are different theorems for the same. All you need to do is to understand why it is the way it is. Once you understand them it would be easy for you to solve questions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-11-maths-chapter-30-exercise-304\"><\/span>RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.4<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Exercise &#8211; 30.4 covers only one concept i.e. Product rule for differentiation.<\/p>\n<p>This rule says, Derivative of the product of two functions= [(First Function)* (Derivative of 2<sup>nd<\/sup> function) + (Second function)*(Derivative of first function)]<\/p>\n<p>The second theorem is about the Generalization of the product rule.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-11-maths-chapter-30-exercise-305\"><\/span>RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Exercise &#8211; 30.5 is all about using all the concepts covered till 30.4. This exercise will give you sufficient practice for using the concepts together. Along with it, there will be the quotient rule for differentiation.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-11-maths-chapter-30\"><\/span>Access RD Sharma Solutions Class 11 Maths Chapter 30<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"exercise-301-page-no-303\"><\/span>EXERCISE 30.1 PAGE NO: 30.3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Find the derivative of f(x) = 3x at x = 2<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>f(x) = 3x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-1.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 1\" \/><\/p>\n<p><strong>2. Find the derivative of f(x) = x<sup>2<\/sup>\u00a0\u2013 2 at x = 10<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>f(x) = x<sup>2<\/sup>\u00a0\u2013 2<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-2.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 2\" \/><\/p>\n<p>= 0 + 20 = 20<\/p>\n<p>Hence,<\/p>\n<p><em>Derivative of f(x) = x<sup>2<\/sup>\u00a0\u2013 2 at x = 10 is 20<\/em><\/p>\n<p><strong>3. Find the derivative of f(x) = 99x at x = 100.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>f(x) = 99x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-3.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 3\" \/><\/p>\n<p><strong>4. Find the derivative of f(x) = x at x = 1<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>f(x) = x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-4.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 4\" \/><\/p>\n<p><strong>5. Find the derivative of f(x) = cos x at x = 0<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>f(x) = cos x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-5.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 5\" \/><\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-6.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 6\" \/><\/p>\n<p><strong>6. Find the derivative of f(x) = tan x at x = 0<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>f(x) = tan x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-7.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 7\" \/><\/p>\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<p><strong>(iii) 2 cos x at x = \u03c0\/2<\/strong><\/p>\n<p><strong>(iv) sin 2xat x = \u03c0\/2<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i) sin x at x = \u03c0\/2<\/strong><\/p>\n<p>Given:<\/p>\n<p>f (x) = sin x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-8.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 8\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"since-it-is-of-indeterminate-form-let-us-try-to-evaluate-the-limit\"><\/span>[Since it is of indeterminate form, let us try to evaluate the limit.]<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>We know that 1 \u2013 cos x = 2 sin<sup>2<\/sup>(x\/2)<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-9.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 9\" \/><\/p>\n<p><strong>(ii) x at x = 1<\/strong><\/p>\n<p>Given:<\/p>\n<p>f (x) = x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-10.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 10\" \/><\/p>\n<p><strong>(iii) 2 cos x at x = \u03c0\/2<\/strong><\/p>\n<p>Given:<\/p>\n<p>f (x) = 2 cos x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-11.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 11\" \/><\/p>\n<p><strong>(iv) sin 2xat x = \u03c0\/2<\/strong><\/p>\n<p>Solution:<\/p>\n<p>Given:<\/p>\n<p>f (x) = sin 2x<\/p>\n<p>By using the derivative formula,<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-12.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 12\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"since-it-is-of-indeterminate-form-we-shall-apply-the-sandwich-theorem-to-evaluate-the-limit\"><\/span>[Since it is of indeterminate form, we shall apply the sandwich theorem to evaluate the limit.]<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Now, multiply the numerator and denominator by 2, and we get<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-30-derivatives-image-13.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 30 \u2013 Derivatives - image 13\" \/><\/p>\n<hr \/>\n<h2><span class=\"ez-toc-section\" id=\"important-topics-from-rd-sharma-solutions-class-11-maths-chapter-30-derivatives\"><\/span>Important Topics from RD Sharma Solutions Class 11 Maths Chapter 30- Derivatives<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The chapter is not very simple, it requires a lot of practice and patience.<\/p>\n<p>The important topics are listed below:<\/p>\n<ul>\n<li>Product rule<\/li>\n<li>Division Rule<\/li>\n<li>Quotient Rule for Differentiation<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"key-take-away-from-class11-maths-chapter-30-derivatives-rd-sharma-solutions\"><\/span><strong>Key Take Away from Class11 Maths Chapter 30- Derivatives RD Sharma Solutions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>Don\u2019t mug up things because it\u2019s important to understand the concepts.<\/li>\n<li>Consider this book as a help book.<\/li>\n<li>Go step-by-step while solving questions.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class11-maths-chapter-30\"><\/span>RD Sharma Solutions Class11 Maths Chapter 30<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If you are done with this much, it is sufficient for Chapter 30. Once done, it becomes easy for you to solve any type of question. Do let us know if you have any queries about the chapter. We would love to answer all your queries. All the best for your <a href=\"https:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">CBSE<\/a> class 11 examinations.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-11-maths-chapter-30\"><\/span>FAQs on RD Sharma Solutions Class 11 Maths Chapter 30<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630069627613\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-the-solutions-rd-sharma-solutions-class-11-maths-chapter-30-relevant\"><\/span>Are the solutions RD Sharma Solutions Class 11 Maths Chapter 30\u00a0relevant?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The solutions are relevant as they are designed by the subject matter experts. \u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630069681274\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-it-even-beneficial-to-study-rd-sharma-solutions-class-11-maths-chapter-30\"><\/span>Is it even beneficial to study RD Sharma Solutions Class 11 Maths Chapter 30?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, your preparation will be strengthened with this amazing help book. All your questions will be answered by this book.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630069725343\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-access-the-rd-sharma-solutions-class-11-maths-chapter-30-pdf-offline\"><\/span>Can I access the RD Sharma Solutions Class 11 Maths Chapter 30 PDF offline?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Once you have downloaded the PDF online, you can access it offline as well.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives:\u00a0Derivatives are considered to be among the most important chapters of Class 11 mathematics. You will learn to use limits (which you have studied in the previous chapter) with derivatives. This chapter will also help you in your Class 12 Maths exam prep. Therefore, it is &#8230; <a title=\"RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives (Updated For 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-30-derivatives\/\" aria-label=\"More on RD Sharma Solutions Class 11 Maths Chapter 30 &#8211; Derivatives (Updated For 2024)\">Read more<\/a><\/p>\n","protected":false},"author":243,"featured_media":121250,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3428,73334],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/64129"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=64129"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/64129\/revisions"}],"predecessor-version":[{"id":501111,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/64129\/revisions\/501111"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/121250"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=64129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=64129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=64129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}