*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 BYJU’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 – Limits and Derivatives are based on the following topics:
- Derivatives
- Algebra of derivative of functions
- 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.
Download the 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
Also, explore – NCERT Class 11 Solutions
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 the first principle,
= 99
4. 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
Solution:
(i) Let f (x) = x3 – 27
From the first principle,
(ii) Let f (x) = (x – 1) (x – 2)
From the first principle,
(iii) Let f (x) = 1 / x2
From the first principle, we get
(iv) Let f (x) = x + 1 / x – 1
From the 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 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 – 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
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