RD SHARMA SOLUTION CHAPTER- 30 Derivatives I CLASS 11TH MATHEMATICS-EDUGROW

Table of Contents

Chapter 30 Derivatives Exercise Ex. 30.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7 (i)

Solution 7 (i)

Question 7 (ii)

Solution 7 (ii)

Question 7 (iii)

Solution 7 (iii)

Question 7(iv)

Solution 7(iv)

Chapter 30 Derivatives Exercise Ex. 30.2

Question 1(i)

Solution 1(i)

Question 1 (ii)

Solution 1 (ii)

Question 1 (iii)

Solution 1 (iii)

Question 1 (iv)

Solution 1 (iv)

Question 1 (v)

Solution 1 (v)

Question 1 (vi)

Solution 1 (vi)

Question 1 (vii)

Solution 1 (vii)

Question 1 (viii)

Solution 1 (viii)

Question 1 (ix)

Solution 1 (ix)

Question 1 (x)

Solution 1 (x)

Question 1 (xi)

Solution 1 (xi)

Question 1 (xii)

Solution 1 (xii)

Question 1 (xiii)

Solution 1 (xiii)

Question 1 (xiv)

Solution 1 (xiv)

Question 2 (i)

Solution 2 (i)

Question 2 (ii)

Solution 2 (ii)

Question 2 (iii)

Solution 2 (iii)

Question 2 (iv)

Solution 2 (iv)

Question 2(ix)

Solution 2(ix)

Question 2(x)

Solution 2(x)

Question 2(xi)

Solution 2(xi)

Question 3 (vii)

Solution 3 (vii)

Question 3 (viii)

Solution 3 (viii)

Question 3 (ix)

Solution 3 (ix)

Question 3 (x)

Solution 3 (x)

Question 3 (xi)

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

Question 3 (xii)

Solution 3 (xii)

Question 3 (i)

Solution 3 (i)

Question 3 (ii)

Solution 3 (ii)

Question 3 (iii)

Solution 3 (iii)

Question 3 (iv)

Solution 3 (iv)

Question 3 (v)

Solution 3 (v)

Question 3 (vi)

Solution 3 (vi)

Question 4 (i)

Solution 4 (i)

Question 4 (ii)

Solution 4 (ii)

Question 4 (iii)

Solution 4 (iii)

Question 4 (iv)

Solution 4 (iv)

Question 5(i)

Solution 5(i)

Question 5 (ii)

Solution 5 (ii)

Question 5 (iii)

Solution 5 (iii)

Question 5(iv)

Solution 5(iv)

Question 6 (i)

Solution 6 (i)

Question 6 (ii)

Solution 6 (ii)

Question 6(iii)

Solution 6(iii)

Question 6(iv)

Solution 6(iv)

Question 1(xv)

Solution 1(xv)

Question 2(v)

Differentiate -x using first principles.Solution 2(v)

Question 2(vi)

Differentiate (-x)^-1 using first principles.Solution 2(vi)

Question 2(vii)

Differentiate sin(x + 1) using first principles.Solution 2(vii)

Question 2(viii)

Differentiate cos using first principles.Solution 2(viii)

Chapter 30 Derivatives Exercise Ex. 30.3

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Defferentiate f (x) = $log open parentheses fraction numerator 1 over denominator square root of straight x end fraction close parentheses plus 5 straight x to the power of straight a minus 3 straight a to the power of straight x plus 3 square root of straight x squared end root plus 6 fourth root of straight x to the power of negative 3 end exponent end root with space respect space to space straight x.$ 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

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Chapter 30 Derivatives Exercise Ex. 30.4

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Differentiate the following functions with respect to x:

Solution 25

Question 26

Differentiate the following functions with respect to x:

(ax + b)ⁿ (cx + d)^mSolution 26

Question 27

Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answer are the same.Solution 27