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

*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 12.

Class 11 students who solve with the NCERT Solutions can score good marks in the exams. To help them to score score good marks in the board examinations, the subject experts at BYJUâ€™S have provided the solutions to all the questions present in all the chapters of Class 11. On this page, students can see the solutions to the second exercise of Chapter 13 Class 11 Maths. Chapter 13 Limits and Derivatives of Class 11 Maths is included in the CBSE Syllabus for the 2023-24 session. Exercise 13.2 of NCERT Solutions for Class 11 Maths Chapter 13 â€“ 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 board examinations. Downloading the NCERT Solutions of Class 11 Maths now and practising them well will help them in reaching their goal with ease.

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### Access Other Exercise Solutions of Class 11 Maths Chapter 13 â€“ Limits and Derivatives

Exercise 13.1 Solutions: 32 Questions

Miscellaneous Exercise on Chapter 13 Solutions: 30 Questions

Also, explore â€“ NCERT Class 11 Solutions

#### Access Solutions for Class 11 Maths Chapter 13 Exercise 13.2

1. Find the derivative of x2â€“ 2 at x = 10.

Solution:

Let f (x) = x2 â€“ 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 the first principle,

= 99

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

(i) x3 â€“ 27

(ii) (x â€“ 1) (x â€“ 2)

(iii) 1 / x2

(iv) x + 1 / x â€“ 1

Solution:

(i) Let f (x) = x3 â€“ 27

From the first principle,

(ii) Let f (x) = (x â€“ 1) (x â€“ 2)

From the first principle,

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

From the first principle, we get

(iv) Let f (x) = x + 1 / x â€“ 1

From the first principle, we get

5. For the functionÂ  , prove that fâ€™ (1) =100 fâ€™ (0).

Solution:

6. Find the derivative ofÂ Â for some fixed real number a.

Solution:

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

(ii) (ax2 + b)2

(iii) x â€“ a / x â€“ b

Solution:

(i) (x â€“ a) (x â€“ b)

(ii) (ax2 + b)2

= 4ax (ax2 + b)

(iii) x â€“ a / x â€“ b

8. Find the derivative ofÂ Â for some constant a.

Solution:

9. Find the derivative of

(i) 2x â€“ 3 / 4

(ii) (5x3 + 3x â€“ 1) (x â€“ 1)

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

(iv) x5 (3 â€“ 6x-9)

(v) x-4 (3 â€“ 4x-5)

(vi) (2 / x + 1) â€“ x2 / 3x â€“ 1

Solution:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

10. Find the derivative of cos x from the 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 â€“ 6 cos x + 7

(vii) 2 tan x â€“ 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 â€“ 6 cos x + 7

(vii) 2 tan x â€“ 7 sec x