Chapter 11 : Differentiation - Rd Sharma Solutions for Class 12-science Maths CBSE

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

On TopperLearning, you can find study resources such as sample papers, mock tests, Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals, and more. Also, you can practise the Maths problems by going through the solutions given by our experts.

Maths is considered as one of the most difficult subjects in CBSE Class 12 Science. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve problems and score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Solve those doubts by asking an expert through the “Undoubt” feature on the student dashboard.

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Chapter 11 - Differentiation Exercise Ex. 11.1

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

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10


Chapter 11 - Differentiation Exercise Ex. 11.2

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


T h u s comma space fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator cos squared x end fraction plus fraction numerator sin x over denominator cos squared x end fraction
rightwards double arrow fraction numerator d y over denominator d x end fraction equals s e c squared x plus tan x s e c x
rightwards double arrow fraction numerator d y over denominator d x end fraction equals s e c x open square brackets tan x plus s e c x close square brackets

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

Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31

Question 32
Solution 32
Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
Question 39
Solution 39

Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44
Solution 44
Question 45
Solution 45


Question 46
Solution 46
Question 47
Solution 47
Question 48
Solution 48

Question 49
Solution 49
Question 50
Solution 50
Question 51
Solution 51
Question 52
Solution 52
Question 53

Differentiate the following functions with respect to x:

Solution 53

Question 54
Solution 54
Question 55
Solution 55
Question 56
Solution 56
Question 57
Solution 57
Question 58
Solution 58
Question 59
Solution 59
Question 60
Solution 60
Question 61
Solution 61

Question 62
Solution 62
Question 63
Solution 63

Question 64
Solution 64
Question 65
Solution 65

Question 66
Solution 66
Question 67
Solution 67
Question 68
Solution 68
Question 69
Solution 69
Question 70
Solution 70
Question 71
Solution 71
Question 72
Solution 72
Question 73
Solution 73

Question 74
Solution 74

Chapter 11 - Differentiation Exercise Ex. 11.3

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
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
Solution 25
Question 26
Solution 26

Question 27
Solution 27

Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35

Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38

Question 39

Solution 39
Question 40
Solution 40

Question 41
Solution 41
Question 42
Solution 42

Question 43
Solution 43
Question 44
Solution 44

Question 45
Solution 45

Question 46

Solution 46

Question 47
Solution 47

Question 48

Solution 48

Chapter 11 - Differentiation Exercise Ex. 11.4

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
Solution 25


Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30

Chapter 11 - Differentiation Exercise Ex. 11.5

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
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28

Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31

Question 32

Solution 32

Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42

Question 43
Solution 43
Question 44
Solution 44
Question 45
Solution 45
Question 46
Solution 46

Question 47
Solution 47

Question 48
Solution 48
Question 49
Solution 49
Question 50
Solution 50

Question 51
Solution 51
Question 52
Solution 52
Question 53
Solution 53
Question 54
Solution 54
Question 55
Solution 55
Question 56
Solution 56
Question 57

Solution 57

Question 58
Solution 58
Question 59
Solution 59
Question 60
Solution 60
Question 61
Solution 61

Question 62
Solution 62
Question 63
Solution 63

Question 64
Solution 64
Question 65

Solution 65

Question 66

Solution 66

Question 67

Solution 67

Question 68

Solution 68

Question 69

Solution 69

Chapter 11 - Differentiation Exercise Ex. 11.6

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

Chapter 11 - Differentiation Exercise Ex. 11.7

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

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Chapter 11 - Differentiation Exercise Ex. 11.8

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3

Question 4
Solution 4
Question 5

begin mathsize 12px style Differentiate space sin to the power of negative 1 end exponent square root of 1 minus straight x squared end root with space respect space to space cos to the power of negative 1 end exponent straight x comma space if
straight x space element of space open parentheses negative 1 comma space 0 close parentheses end style

Solution 5

Question 6

begin mathsize 12px style Differentiate space sin to the power of negative 1 end exponent open parentheses 4 straight x square root of 1 minus 4 straight x squared end root close parentheses space space with space space respect space to space square root of 1 minus 4 straight x squared end root comma space if
straight x space element of open parentheses fraction numerator 1 over denominator negative 2 square root of 2 end fraction comma fraction numerator 1 over denominator 2 square root of 2 end fraction close parentheses end style

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


Chapter 11 - Differentiation Exercise MCQ

Question 1

If f(x) = logx2 (log x), then f' (x) at x = e is

a. 0

b. 1

c. 1/e

d. 1/2 e

Solution 1

Correct option: (d)

 

  

Question 2

The differential coefficient of f (log x) with respect to x, where f (x) = log x is

Solution 2

Correct option: (c)

  

Question 3

Solution 3

Correct option: (a)

  

Question 4

Differential coefficient of sec (tan-1 x) is

Solution 4

Correct option: (d)

  

Question 5

Solution 5

Correct option: (d)

  

Question 6

Solution 6

Correct option: (a)

  

Question 7

Solution 7

Correct option: (d)

  

Question 8

Given f(x) = 4x8, then

Solution 8

Correct option: (c)

  

 

Question 9

Solution 9

Correct option: (d)

  

Question 10

Solution 10

Correct option:(a)

  

Question 11

Solution 11

Correct option: (a)

  

Question 12

Solution 12

Correct option: (c)

  

Question 13

Solution 13

Correct option: (d)

  

Question 14

  1. 1/2
  2. x

 

  1. 1
Solution 14

Correct option: (d)

  

Question 15

Solution 15

Correct option: (b)

  

Question 16

Solution 16

Correct option: (a)

  

Question 17

Solution 17

Correct option: (d)

  

Question 18

Solution 18

Correct option: (a)

  

Question 19

Solution 19

Correct option: (b)

  

Question 20

The derivative of cos-1 (2x2 - 1) with respect to cos-1 x is

Solution 20

Correct option: (a)

  

Question 21

Solution 21

Correct option: (b)

  

Question 22

Solution 22

Correct option: (c)

  

Question 23

Solution 23

Correct option:(d)

  

Question 24

Solution 24

Correct option: (a)

  

Question 25

Solution 25

Correct option: (b)

  

Question 26

Solution 26

Correct option: (c)

  

Question 27

Solution 27

Correct option:(a)

  

Question 28

Solution 28

Correct option: (b)

  

Question 29

Solution 29

Correct option: (b)

  

Question 30

Solution 30

Correct option: (a) 

  

 

Question 31

Solution 31

Correct option: (b)

  

Question 32

Solution 32

Correct option: (a)

  

Question 33

Solution 33

Correct option: (c)

  

Chapter 11 - Differentiation Exercise Ex. 11VSAQ

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

begin mathsize 12px style If space straight y equals sin to the power of negative 1 end exponent open parentheses sin space straight x close parentheses comma negative straight pi over 2 less or equal than straight x less or equal than straight pi over 2. Then comma space write space the space value space of space dy over dx for space straight x element of open parentheses negative straight pi over 2 comma straight pi over 2 close parentheses. end style

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

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Write the derivative of sin x with respect to cos x.

Solution 28

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Why CBSE Class 12 Science Maths solutions are important?

Maths is a subject which requires practising a variety of problems to understand concepts clearly. By solving as many problems as you can, you’ll be able to train your brain in thinking the logical way to solve maths problems. For practising problems, study materials such as sample papers, previous year papers, and NCERT solutions are needed.

Some of the best Maths experts work with us to give you the best solutions for Maths textbook questions and sample paper questions. Chapter-wise NCERT solutions for Class 12 Science Maths can be easily accessible on TopperLearning. Use these solutions to practise problems based on concepts such as direction ratios, probability, area between lines, inverse trigonometric functions, and more.

To prepare for your Maths exam, you need to attempt solving different kinds of Maths questions. One of the best ways to assess your problem-solving abilities is to attempt solving previous year papers with a set timer. Our Maths solutions will come in handy to help you with checking your answers and thus, improving your learning experience. So, to score more marks in your Class 12 board exams, use our Maths solutions that will enable you with the appropriate preparation.