NCERT Solutions for Class 11 Maths chapter-13 Limits and Derivatives Miscellaneous Exercise

NCERT Solutions for Class 11 Maths chapter-13 Limits and Derivatives Miscellaneous Exercise

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

Academic team of Physics Wallah developed step by step NCERT Solutions for Class 11 Maths Chapter-13 Limits and Derivatives Miscellaneous Exercise according to recommendations and Guideline of CBSE. You can download and share NCERT Solutions for Class 11 Maths.

NCERT Solutions for Class 11 Maths Miscellaneous Exercise

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

(i) −x

( ii) (−x) ⁻¹

( iii) sin(x+1)

(iii)cos(x−π/8)

Solution :
(i)Given:f(x) = -x  then

(ii)Given:

then

(iii)Given: f ( x ) = sin ( x + 1)

then

(iv)Given:

then

Question 2. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x + a)

Solution :

f(x) = (x + a)

Accordingly,

By first principle,

Question 3. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (px+q)(r/x+s)

Solution :
Given:f(x) =

Question 4. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):(ax+b)(cx+d) ²

Solution :
Given:f(x) = (ax+b)(cx+d) ²

Question 5. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 6. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 7. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 8. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 9. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 10. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 11. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 12. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax+b) ⁿ

Solution :

Question 13. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):(ax+b) ⁿ (cx+d) ^m

Solution :

since,

Question 14. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):sin (x + a)

Solution :

Question 15. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosec x cot x

Solution :

Question 16. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 17. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 18. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 19. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): sin ⁿ x

Solution :

Question 20. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 21. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 22. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): x ⁴ (5 sin x – 3 cos x)

Solution :

Question 23. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):  (x ² +1)cosx

Solution :

Question 24. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax ² + sinx)(p + qcosx)

Solution :

Question 25. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x+cosx) (x−tanx)

Solution :

Question 26. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 27. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 28. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :

Question 29. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x + sec x) (x – tan x)

Solution :
let f(x) = (x + sec x) (x – tan x)

By product rule,

Q uestion 30. Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Solution :