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

Solution:

Let f (x) = x

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

Solution:

Let f (x) = 99x,

From first principle = 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  (ii) Let f (x) = (x – 1) (x – 2)

From first principle  (iii) Let f (x) = 1 / x2

From first principle, we get  (iv) Let f (x) = x + 1 / x – 1

From first principle, we get  5. For the function .Prove that f’ (1) =100 f’ (0).

Solution:  6. Find the derivative of for some fixed real number a.

Solution: 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) (ii) (ax2 + b)2 = 4ax (ax2 + b)

(iii) x – a / x – b   8. Find the derivative of for some constant a.

Solution: 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) (ii) (iii)  (iv) (v)  (vi)  10. Find the derivative of cos x from first principle

Solution:    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  (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    