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

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

NCERT Solutions for Class 11 Maths Chapter 13 contains solutions for all miscellaneous exercise questions. Class 11 Maths Chapter 13, Limits and Derivatives, is included in the CBSE Syllabus for the 2023-24 academic year. NCERT Solutions help students identify their strengths and weaknesses, which will help them improve their weak areas. It definitely boosts their confidence levels and helps them to score well. The Miscellaneous Exercise of NCERT Solutions for Class 11 Maths Chapter 13 â€“ Limits and Derivatives are based on the following topics:

1. Intuitive Idea of Derivatives
2. Limits
3. Limits of Trigonometric Functions
4. Derivatives

Students can download theseÂ NCERT Solutions of Class 11 Maths from BYJUâ€™S in PDF, in the link given below, and practise them to prepare for the annual examinations more effectively. The solutions provided here contain the answers to all the questions given in the NCERT Textbook of Class 11 Maths.

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

Exercise 13.1 Solutions 32 Questions

Exercise 13.2 Solutions 11 Questions

Also, explore â€“ NCERT Class 11 Solutions

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

1. Find the derivative of the following functions from the first principle:

(i) â€“xÂ

(ii) (â€“x)â€“1Â

(iii) sin (xÂ + 1)

(iv)Â

Solution:

(ii) (-x)-1

= 1 / x2

(iii) sin (x + 1)

(iv)

We get,

Find the derivative of the following functions (It is to be understood that a,Â b,Â c,Â d,Â p, q,Â rÂ andÂ s are fixed non-zero constants, andÂ mÂ andÂ nÂ are integers):

2. (xÂ +Â a)

Solution:

3. (px + q) (r / x + s)

Solution:

4. (axÂ +Â b) (cxÂ +Â d)2

Solution:

5. (ax + b) / (cx + d)

Solution:

6. (1 + 1 / x) / (1 â€“ 1 / x)

Solution:

7. 1 / (ax2 + bx + c)

Solution:

8. (ax + b) / px2 + qx + r

Solution:

9. (px2 + qx + r) / ax + b

Solution:

10. (a / x4) â€“ (b / x2) + cos x

Solution:

11.

Solution:

12. (ax + b)n

Solution:

13. (axÂ +Â b)nÂ (cxÂ +Â d)m

Solution:

14. sin (xÂ +Â a)

Solution:

15. cosecÂ xÂ cotÂ x

Solution:

So, we get

16.

Solution:

17.

Solution:

18.

Solution:

19. sinnÂ x

Solution:

20.

Solution:

21.

Solution:

22. x4Â (5 sinÂ xÂ â€“ 3 cosÂ x)

Solution:

23. (x2Â + 1) cosÂ x

Solution:

24. (ax2Â + sinÂ x) (pÂ +Â qÂ cosÂ x)

Solution:

25.

Solution:

26.

Solution:

27.

Solution:

28.

Solution:

29. (xÂ + secÂ x) (xÂ â€“ tanÂ x)

Solution:

30.

Solution: