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RD Sharma Solution for Class 11 Science Mathematics Chapter 30 - Derivatives

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 11 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 30 - Derivatives.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 11 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 11 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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RD Sharma Solution for Class 11 Science Mathematics Chapter 30 - Derivatives Page/Excercise 30.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7 (i)

Solution 7 (ii)

Solution 7 (iii)

Solution 7(iv)

RD Sharma Solution for Class 11 Science Mathematics Chapter 30 - Derivatives Page/Excercise 30.2

Solution 1(i)

Solution 1 (ii)

Solution 1 (iii)

Solution 1 (iv)

Solution 1 (v)

Solution 1 (vi)

Solution 1 (vii)

Solution 1 (viii)

Solution 1 (ix)

Solution 1 (x)

Solution 1 (xi)

Solution 1 (xii)

Solution 1 (xiii)

Solution 1 (xiv)

Solution 2 (i)

Solution 2 (ii)

Solution 2 (iii)

Solution 2 (iv)

Solution 2(ix)

Solution 2(x)

Solution 2(xi)

Solution 3 (vii)

Solution 3 (viii)

Solution 3 (ix)

Solution 3 (x)

Solution 3 (xi)

f left parenthesis x right parenthesis equals a to the power of square root of x end exponent equals e to the power of square root of x log a end exponent

f to the power of comma left parenthesis x right parenthesis equals limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction
space space space space space space space space equals limit as h rightwards arrow 0 of fraction numerator e to the power of square root of x plus h end root log a end exponent minus e to the power of square root of x log a end exponent over denominator h end fraction
space space space space space space space space equals limit as h rightwards arrow 0 of e to the power of square root of x log a end exponent fraction numerator e to the power of square root of x plus h end root log a minus square root of x log a end exponent minus 1 over denominator h end fraction
space space space space space space space space equals limit as h rightwards arrow 0 of e to the power of square root of x log a end exponent fraction numerator e to the power of open parentheses square root of x plus h end root minus square root of x close parentheses log a end exponent minus 1 over denominator h end fraction
text Multiply   numerator   and   denominator   by end text space open parentheses square root of x plus h end root minus square root of x close parentheses log a
f to the power of comma left parenthesis x right parenthesis space equals limit as h rightwards arrow 0 of e to the power of square root of x log a end exponent fraction numerator e to the power of open parentheses square root of x plus h end root minus square root of x close parentheses log a end exponent minus 1 over denominator h open parentheses square root of x plus h end root minus square root of x close parentheses log a end fraction open parentheses square root of x plus h end root minus square root of x close parentheses log a
space space space space space space space space equals e to the power of square root of x log a end exponent limit as h rightwards arrow 0 of fraction numerator e to the power of open parentheses square root of x plus h end root minus square root of x close parentheses log a end exponent minus 1 over denominator open parentheses square root of x plus h end root minus square root of x close parentheses log a end fraction limit as h rightwards arrow 0 of log a fraction numerator open parentheses square root of x plus h end root minus square root of x close parentheses over denominator h end fraction
space space space space space space space space space equals e to the power of square root of x log a end exponent limit as h rightwards arrow 0 of log a fraction numerator open parentheses square root of x plus h end root minus square root of x close parentheses over denominator h end fraction

text Multiply   numerator   and   denominator   by end text space open parentheses square root of x plus h end root plus square root of x close parentheses
space f to the power of comma left parenthesis x right parenthesis equals e to the power of square root of x log a end exponent limit as h rightwards arrow 0 of log a fraction numerator open parentheses square root of x plus h end root minus square root of x close parentheses over denominator h open parentheses square root of x plus h end root plus square root of x close parentheses end fraction open parentheses square root of x plus h end root plus square root of x close parentheses
equals e to the power of square root of x log a end exponent limit as h rightwards arrow 0 of log a fraction numerator h over denominator h open parentheses square root of x plus h end root plus square root of x close parentheses end fraction
equals e to the power of square root of x log a end exponent fraction numerator log a over denominator 2 square root of x end fraction
equals fraction numerator a square root of blank to the power of x end root over denominator 2 square root of x end fraction log subscript e a

 

Solution 3 (xii)

Solution 3 (i)

Solution 3 (ii)

Solution 3 (iii)

Solution 3 (iv)

Solution 3 (v)

Solution 3 (vi)

Solution 4 (i)

Solution 4 (ii)

Solution 4 (iii)

Solution 4 (iv)

Solution 5(i)

Solution 5 (ii)

Solution 5 (iii)

Solution 5(iv)

Solution 6 (i)

Solution 6 (ii)

Solution 6(iii)

Solution 6(iv)

Solution 1(xv)

Solution 2(v)

  

Solution 2(vi)

  

Solution 2(vii)

  

Solution 2(viii)

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 30 - Derivatives Page/Excercise 30.3

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

fraction numerator d over denominator a x end fraction open curly brackets log open parentheses fraction numerator 1 over denominator square root of x end fraction close parentheses plus 5 x to the power of a minus 3 a to the power of x plus 3 root of x squared end root plus 6 4 root of x to the power of minus 3 end exponent end root close curly brackets
equals fraction numerator d over denominator a x end fraction log open parentheses fraction numerator 1 over denominator square root of x end fraction close parentheses plus 5 fraction numerator d over denominator a x end fraction open parentheses x to the power of a close parentheses minus 3 open parentheses a to the power of x close parentheses plus fraction numerator d over denominator a x end fraction open parentheses 3 root of x squared end root close parentheses plus 6 fraction numerator d over denominator a x end fraction open parentheses 4 root of x to the power of minus 3 end exponent end root close parentheses
equals fraction numerator minus 1 over denominator 2 end fraction 1 over x plus 5 a x to the power of a minus 1 end exponent minus 3 a to the power of x log a plus fraction numerator 2 x to the power of begin display style bevelled fraction numerator minus 1 over denominator 3 end fraction end style end exponent over denominator 3 end fraction plus 6 x to the power of bevelled fraction numerator minus 7 over denominator 4 end fraction end exponent open parentheses bevelled fraction numerator minus 3 over denominator 4 end fraction close parentheses
equals fraction numerator minus 1 over denominator 2 x end fraction plus 5 a x to the power of a minus 1 end exponent minus 3 a to the power of x log a plus fraction numerator 2 x to the power of begin display style bevelled fraction numerator minus 1 over denominator 3 end fraction end style end exponent over denominator 3 end fraction minus 9 over 2 x to the power of bevelled fraction numerator minus 7 over denominator 4 end fraction end exponent

 

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

RD Sharma Solution for Class 11 Science Mathematics Chapter 30 - Derivatives Page/Excercise 30.4

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

  

Solution 26

  

Solution 27

  

Solution 28(i)

  

Solution 28(ii)

  

Solution 28(iii)

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 30 - Derivatives Page/Excercise 30.5

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

fraction numerator d over denominator d x end fraction open parentheses fraction numerator x to the power of n over denominator sin x end fraction close parentheses
equals x to the power of n fraction numerator d over denominator d x end fraction open parentheses sin x close parentheses to the power of minus 1 end exponent plus fraction numerator 1 over denominator sin x end fraction fraction numerator d over denominator d x end fraction open parentheses x to the power of n close parentheses
equals x to the power of n fraction numerator minus 1 over denominator sin squared x end fraction plus fraction numerator 1 over denominator sin x end fraction n x to the power of n minus 1 end exponent
equals fraction numerator sin x left parenthesis n x to the power of n minus 1 end exponent right parenthesis minus x to the power of n left parenthesis cos x right parenthesis over denominator sin squared x end fraction

Solution 29

Solution 30

Syntax error from line 1 column 1707 to line 1 column 1712. Unexpected '</mi>'.

RD Sharma Solution for Class 11 Science Mathematics Chapter 30 - Derivatives Page/Excercise 30VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

text for   x = 2 end text

open vertical bar x minus 1 close vertical bar equals left parenthesis x minus 1 right parenthesis space space space text and     end text open vertical bar x minus 3 close vertical bar equals minus open parentheses x minus 3 close parentheses

fraction numerator d over denominator d x end fraction open parentheses open vertical bar x minus 1 close vertical bar plus open vertical bar x minus 3 close vertical bar close parentheses
equals fraction numerator d over denominator d x end fraction open parentheses open vertical bar x minus 1 close vertical bar close parentheses plus fraction numerator d over denominator d x end fraction open parentheses open vertical bar x minus 3 close vertical bar close parentheses
equals fraction numerator d over denominator d x end fraction open parentheses x minus 1 close parentheses plus fraction numerator d over denominator d x end fraction open parentheses minus left parenthesis x minus 3 right parenthesis close parentheses
equals fraction numerator d over denominator d x end fraction open parentheses x minus 1 close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 3 minus x right parenthesis close parentheses
equals 1 minus 1
equals 0

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

text We   have end text
y equals 1 plus x plus x squared plus x cubed plus horizontal ellipsis
space space space equals open parentheses 1 minus x close parentheses to the power of minus 1 end exponent

fraction numerator d y over denominator d x end fraction equals fraction numerator d over denominator d x end fraction open parentheses 1 minus x close parentheses to the power of minus 1 end exponent
space space space space space space space space equals open parentheses minus 1 close parentheses open parentheses 1 minus x close parentheses to the power of minus 2 end exponent cross times open parentheses minus 1 close parentheses
space space space space space space space space equals open parentheses 1 minus x close parentheses to the power of minus 2 end exponent
space space space space space space space space equals 1 over open parentheses 1 minus x close parentheses squared

Solution 14

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 11. Access the CBSE Class 11 Mathematics Chapter 30 - Derivatives for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 30 - Derivatives.

Text Book Solutions

CBSE XI Science - Mathematics

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