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NCERT · Class 11 · Maths

Chapter 13: Limits and Derivatives Exercise 13.2

Practice each question, then open the answer or worked solution.

Questions

11 questions
Q1Written answer

Find the derivative of x2– 2 at x = 10.

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Worked solution

Let f (x) = x2 – 2

NCERT Solutions Mathematics Class 11 Chapter 13 - 102

NCERT Solutions Mathematics Class 11 Chapter 13 - 103

Q2Written answer

Find the derivative of x at x = 1.

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Worked solution

Let f (x) = x

Then,

NCERT Solutions Mathematics Class 11 Chapter 13 - 104

NCERT Solutions Mathematics Class 11 Chapter 13 - 105

Q3Written answer

Find the derivative of 99x at x = l00.

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Worked solution

Let f (x) = 99x,

From the first principle,

NCERT Solutions Mathematics Class 11 Chapter 13 - 106

= 99

Q4Written answer

Find the derivative of the following functions from the first principle.

(i) x3 – 27

(ii) (x – 1) (x – 2)

(iii) 1 / x2

(iv) x + 1 / x – 1

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Worked solution

(i) Let f (x) = x3 – 27

From the first principle,

NCERT Solutions Mathematics Class 11 Chapter 13 - 107

NCERT Solutions Mathematics Class 11 Chapter 13 - 108

(ii) Let f (x) = (x – 1) (x – 2)

From the first principle,

NCERT Solutions Mathematics Class 11 Chapter 13 - 109

NCERT Solutions Mathematics Class 11 Chapter 13 - 110

(iii) Let f (x) = 1 / x2

From the first principle, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 111

NCERT Solutions Mathematics Class 11 Chapter 13 - 112

(iv) Let f (x) = x + 1 / x – 1

From the first principle, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 113

NCERT Solutions Mathematics Class 11 Chapter 13 - 114

Q5Written answer

For the function NCERT Solutions Mathematics Class 11 Chapter 13 - 115 , prove that f’ (1) =100 f’ (0).

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Worked solution

NCERT Solutions Mathematics Class 11 Chapter 13 - 116

NCERT Solutions Mathematics Class 11 Chapter 13 - 117

Q6Written answer

Find the derivative of NCERT Solutions Mathematics Class 11 Chapter 13 - 118 for some fixed real number a.

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Worked solution

NCERT Solutions Mathematics Class 11 Chapter 13 - 119

Q7Written answer

For some constants a and b, find the derivative of
(i) (x − a) (x − b)

(ii) (ax2 + b)2

(iii) x – a / x – b

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Worked solution

(i) (x – a) (x – b)

NCERT Solutions Mathematics Class 11 Chapter 13 - 120

(ii) (ax2 + b)2

NCERT Solutions Mathematics Class 11 Chapter 13 - 121

= 4ax (ax2 + b)

(iii) x – a / x – b

NCERT Solutions Mathematics Class 11 Chapter 13 - 122

NCERT Solutions Mathematics Class 11 Chapter 13 - 123

NCERT Solutions Mathematics Class 11 Chapter 13 - 124

Q8Written answer

Find the derivative of NCERT Solutions Mathematics Class 11 Chapter 13 - 125 for some constant a.

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Worked solution

NCERT Solutions Mathematics Class 11 Chapter 13 - 126

Q9Written answer

Find the derivative of

(i) 2x – 3 / 4

(ii) (5x3 + 3x – 1) (x – 1)

(iii) x-3 (5 + 3x)

(iv) x5 (3 – 6x-9)

(v) x-4 (3 – 4x-5)

(vi) (2 / x + 1) – x2 / 3x – 1

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Worked solution

(i)

NCERT Solutions Mathematics Class 11 Chapter 13 - 127

(ii)

NCERT Solutions Mathematics Class 11 Chapter 13 - 128

(iii)

NCERT Solutions Mathematics Class 11 Chapter 13 - 129

NCERT Solutions Mathematics Class 11 Chapter 13 - 130

(iv)

NCERT Solutions Mathematics Class 11 Chapter 13 - 131

(v)

NCERT Solutions Mathematics Class 11 Chapter 13 - 132

NCERT Solutions Mathematics Class 11 Chapter 13 - 133

(vi)

NCERT Solutions Mathematics Class 11 Chapter 13 - 134

NCERT Solutions Mathematics Class 11 Chapter 13 - 135

Q10Written answer

Find the derivative of cos x from the first principle.

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Worked solution

NCERT Solutions Mathematics Class 11 Chapter 13 - 136

NCERT Solutions Mathematics Class 11 Chapter 13 - 137

NCERT Solutions Mathematics Class 11 Chapter 13 - 138

NCERT Solutions Mathematics Class 11 Chapter 13 - 139