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

Class 11 students who can solve the NCERT solutions get right exposure to acquire good marks. To help you in scoring good marks in the examination, the subject experts at BYJU’S have provided the solutions of all the questions present in all the chapters of Class 11. In this page, you can see the solutions of second exercise of Chapter 13, Class 11.  The Exercise 13.2 of NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives is 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 practicing and preparing for the exam is to score exceptionally well in the examination. Downloading the NCERT Solutions of Class 11 maths now and practicing 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 13.2 Solutions 11 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

From first principle  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    