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

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2.

• Limits and Derivatives Class 11 Ex 13.1

Board	CBSE
Textbook	NCERT
Class	Class 11
Subject	Maths
Chapter	Chapter 13
Chapter Name	Limits and Derivatives
Exercise	Ex 13.2
Number of Questions Solved	11
Category	NCERT Solutions

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

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.

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.

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.

Question 4.
Find the derivative of the following functions from first principle.
(i) x³ – 27
(ii) (x – 1)(x – 2)
(iii)
(iv)
Solution:

Question 5.
For the function

Prove that f'(1) = 100f'(0)
Solution:
We have

Question 6.
Find the derivative of xⁿ + ax^n-1 + a²x^n-2+
…. + a^n-1x + aⁿ for some fixed real number a.
Solution:
Let f(x) = xⁿ + ax^n-1 + a²x^n-2+
…. + a^n-1x + aⁿ
Differentiating (i) with respect to x, we get
f'(x) = nx^n-1 + (n – 1)ax^n-2 + …… + a^n-1

Question 7.
For some constants a and b, find the derivative of
(i) (x – a)(x – b)
(ii) (ax² + b)²
(iii)
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

Question 8.
Find the derivative for some constant a.
Solution:
Let f(x) = ….(i), where a is a constant.
Differentiating (i) with respect to x, we get

Question 9.
Find the derivative of

Solution:
(i) Let f(x) = …(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)

Question 10.
Find the derivative of cos x from first principle.
Solution:
Let f(x) = cos x

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

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