NCERT Solutions Class 11th Maths Chapter 13 – Limits And Derivatives Exercise 13.2

NCERT Solutions Class 11th Maths Chapter 13 – Limits And Derivatives Exercise 13.2

NCERT Solutions Class 11th Maths Chapter 13 – Limits And Derivatives Exercise 13.2

?Chapter – 13?

✍Limits And Derivatives✍

?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 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) (5×3 + 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