NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives Exercise 13.2

*According to the latest update on the term-wise CBSE Syllabus 2021-22, Limits is included in the term – I and Derivatives is included in the term – II.

Class 11 students who can solve with the NCERT Solutions get the right exposure to acquiring good marks in the term-wise exams. To help you in scoring good marks in the term – I and II examinations, the subject experts at BYJU’S have provided the solutions to all the questions present in all the chapters of Class 11. On this page, you can see the solutions of the second exercise of Chapter 13 Class 11 Maths. Chapter 13 Limits and Derivatives of Class 11 Maths is categorized partly under both the term – I and II CBSE Syllabus for the 2021-22 session. Exercise 13.2 of NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives are based on the following topics:

  1. Derivatives
    1. Algebra of derivative of functions
    2. Derivative of polynomials and trigonometric functions

The ultimate goal of all the students practising and preparing for the exam is to score exceptionally well in both the first and second term examinations. Downloading the NCERT Solutions of Class 11 Maths now and practising them well will help the students in reaching the goal with ease.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives Exercise 13.2

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Access Other Exercise Solutions of Class 11 Maths Chapter 13- Limits and Derivatives

Exercise 13.1 Solutions 32 Questions

Miscellaneous Exercise On Chapter 13 Solutions 30 Questions

Access Solutions for Class 11 Maths Chapter 13 Exercise 13.2

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

Solution:

Let f (x) = x2 – 2

NCERT Solutions Mathematics Class 11 Chapter 13 - 102

NCERT Solutions Mathematics Class 11 Chapter 13 - 103

2. Find the derivative of x at x = 1.

Solution:

Let f (x) = x

Then,

NCERT Solutions Mathematics Class 11 Chapter 13 - 104

NCERT Solutions Mathematics Class 11 Chapter 13 - 105

3. Find the derivative of 99x at x = l00.

Solution:

Let f (x) = 99x,

From first principle

NCERT Solutions Mathematics Class 11 Chapter 13 - 106

= 99

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

(i) x3 – 27

(ii) (x – 1) (x – 2)

(iii) 1 / x2

(iv) x + 1 / x – 1

Solution:

(i) Let f (x) = x3 – 27

From 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 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 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 first principle, we get

NCERT Solutions Mathematics Class 11 Chapter 13 - 113

NCERT Solutions Mathematics Class 11 Chapter 13 - 114

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

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 116

NCERT Solutions Mathematics Class 11 Chapter 13 - 117

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

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 119

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

(ii) (ax2 + b)2

(iii) x – a / x – b

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

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

Solution:

NCERT Solutions Mathematics Class 11 Chapter 13 - 126

9. 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

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

10. Find the derivative of cos x from first principle

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

11. Find the derivative of the following functions:

(i) sin x cos x

(ii) sec x

(iii) 5 sec x + 4 cos x

(iv) cosec x

(v) 3 cot x + 5 cosec x

(vi) 5 sin x – 6 cos x + 7

(vii) 2 tan x – 7 sec x

Solution:

(i) sin x cos x

NCERT Solutions Mathematics Class 11 Chapter 13 - 140

NCERT Solutions Mathematics Class 11 Chapter 13 - 141

(ii) sec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 142

NCERT Solutions Mathematics Class 11 Chapter 13 - 143

NCERT Solutions Mathematics Class 11 Chapter 13 - 144

(iii) 5 sec x + 4 cos x

NCERT Solutions Mathematics Class 11 Chapter 13 - 145

(iv) cosec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 146

NCERT Solutions Mathematics Class 11 Chapter 13 - 147

NCERT Solutions Mathematics Class 11 Chapter 13 - 148

(v) 3 cot x + 5 cosec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 149

NCERT Solutions Mathematics Class 11 Chapter 13 - 150

NCERT Solutions Mathematics Class 11 Chapter 13 - 151

NCERT Solutions Mathematics Class 11 Chapter 13 - 152

NCERT Solutions Mathematics Class 11 Chapter 13 - 153

NCERT Solutions Mathematics Class 11 Chapter 13 - 154

NCERT Solutions Mathematics Class 11 Chapter 13 - 155

NCERT Solutions Mathematics Class 11 Chapter 13 - 156

(vi)5 sin x – 6 cos x + 7

NCERT Solutions Mathematics Class 11 Chapter 13 - 157

NCERT Solutions Mathematics Class 11 Chapter 13 - 158

NCERT Solutions Mathematics Class 11 Chapter 13 - 159

(vii) 2 tan x – 7 sec x

NCERT Solutions Mathematics Class 11 Chapter 13 - 160

NCERT Solutions Mathematics Class 11 Chapter 13 - 161

NCERT Solutions Mathematics Class 11 Chapter 13 - 162

NCERT Solutions Mathematics Class 11 Chapter 13 - 163

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