# NCERT Solutions For Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2

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

NCERT TEXTBOOK EXERCISES

Ex 13.2 Class 11 Maths Question 1.
Find the derivative of x2 – 2 at x = 10.

Solution:

let f(x) = x2 – 2
Differentiating (i) with respect to x, we get
f'(x) = 2x
At x = 10, f'(10) = 2(10) = 20.

Ex 13.2 Class 11 Maths Question 2.
Find the derivative of 99x at x = 10.

Solution:

let f(x) = 99x
Differentiating (i) with respect to x, we get
f'(x) = 90
At x = 100, f'(100) = 99.

Ex 13.2 Class 11 Maths Question 3.
Find the derivative of x at x = 10.

Solution:

let f(x) = x
Differentiating (i) with respect to x, we get
f'(x) = 1
At x = 1, f'(1) = 1.

Ex 13.2 Class 11 Maths Question 4.
Find the derivative of the following functions from first principle.
(i) x3 – 27
(ii) (x – 1)(x – 2)
(iii) 1/x2
(iv) $\frac { x+1 }{ x-1 }$

Solution:

Ex 13.2 Class 11 Maths Question 5.
For the function

Prove that f'(1) = 100f'(0)

Solution:

We have

Ex 13.2 Class 11 Maths Question 6.
Find the derivative of xn + axn-1 + a2xn-2+
…. + an-1x + an for some fixed real number a.

Solution:

Let f(x) = xn + axn-1 + a2xn-2+
…. + an-1x + an
Differentiating (i) with respect to x, we get
f'(x) = nxn-1 + (n – 1)axn-2 + …… + an-1

Ex 13.2 Class 11 Maths Question 7.
For some constants a and b, find the derivative of
(i) (x – a)(x – b)
(ii) (ax2 + b)2
(iii) $\frac { x-a }{ x-b }$

Solution:

(i) Let f(x) = (x – a)(x – b) ….(1)
Differentiating (1) with respect to x, we get
f'(x) = (x – a)(x – b)’ + (x – a)’ (x – b)
⇒ f'(x) = (x – a) + (x – b) = 2x – a – b

Ex 13.2 Class 11 Maths Question 8.
Find the derivative $\frac { { x }^{ n }-{ a }^{ n } }{ x-a }$ for some constant a.

Solution:

Let f(x) = $\frac { { x }^{ n }-{ a }^{ n } }{ x-a }$ ….(i), where a is a constant.
Differentiating (i) with respect to x, we get

Ex 13.2 Class 11 Maths Question 9.
Find the derivative of

Solution:

(i) Let f(x) = 2x−3/4 …(1)
Differentiating (i) with respect to x, we get
f'(x) = 2·1 – 0 ⇒ f'(x) = 2.
(ii) Let f(x) = 5x3 + 3x – 1)(x – 1)

Ex 13.2 Class 11 Maths Question 10.
Find the derivative of cos x from first principle.

Solution: Let f(x) = cos x

Ex 13.2 Class 11 Maths Question 11.
Find the derivative of the following functions:
(i) sin x cos x
(ii) secx
(iii) 5 secx + 4 cosx
(iv) cosecx
(v) 3 cotx + 5 cosecx
(vi) 5sinx – 6 cosx + 7
(vii) 2 tanx – 7 secx.

Solution:

(i) Let f(x) = sin x cos x … (1)
Differentiating (1) with respect to x, we get

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

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