RD Sharma Solutions for Class 11 Chapter 30 - Derivatives Exercise 30.2

This exercise mainly discusses the concepts based on physical and geometrical interpretation of derivative at a point and differentiation from first principles. For better conceptual knowledge, students can refer to RD Sharma Class 11 Maths Solutions for good results in the board exams. The solutions here are developed by the expert tutors in order to help students secure good marks in the board exams. The RD Sharma Solutions are readily available in the pdf format which can be downloaded easily to start practising offline, for better results.

Download the pdf of RD Sharma Solutions for Class 11 Maths Exercise 30.2 Chapter 30 – Derivatives

 

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Also, access other exercises of RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives

Exercise 30.1 Solutions

Exercise 30.3 Solutions

Exercise 30.4 Solutions

Exercise 30.5 Solutions

Access answers to RD Sharma Solutions for Class 11 Maths Exercise 30.2 Chapter 30 – Derivatives

EXERCISE 30.2 PAGE NO: 30.25

1. Differentiate each of the following from first principles:
(i) 2/x
(ii) 1/√x

(iii) 1/x3

(iv) [x2 + 1]/ x

(v) [x2 – 1] / x

Solution:

(i) 2/x

Given:

f (x) = 2/x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 14

∴ Derivative of f(x) = 2/x is -2x-2

(ii) 1/√x

Given:

f (x) = 1/√x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 15

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 16

∴ Derivative of f(x) = 1/√x is -1/2 x-3/2

(iii) 1/x3

Given:

f (x) = 1/x3

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 17

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 18

∴ Derivative of f(x) = 1/x3 is -3x-4

(iv) [x2 + 1]/ x

Given:

f (x) = [x2 + 1]/ x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 19

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 20

= 1 – 1/x2

∴ Derivative of f(x) = 1 – 1/x2

(v) [x2 – 1] / x

Given:

f (x) = [x2 – 1]/ x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 21

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 22

2. Differentiate each of the following from first principles:

(i) e-x

(ii) e3x

(iii) eax+b

Solution:

(i) e-x

Given:

f (x) = e-x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 23

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 24

(ii) e3x

Given:

f (x) = e3x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 25

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 26

(iii) eax+b

Given:

f (x) = eax+b

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 27

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 28

3. Differentiate each of the following from first principles:

(i) √(sin 2x)

(ii) sin x/x

Solution:

(i) √(sin 2x)

Given:

f (x) = √(sin 2x)

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 29

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 30

(ii) sin x/x

Given:

f (x) = sin x/x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 31

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 32

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 33

4. Differentiate the following from first principles:

(i) tan2 x

(ii) tan (2x + 1)

Solution:

(i) tan2 x

Given:

f (x) = tan2 x

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 34

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 35

(ii) tan (2x + 1)

Given:

f (x) = tan (2x + 1)

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 36

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 37

5. Differentiate the following from first principles:

(i) sin √2x

(ii) cos √x

Solution:

(i) sin √2x

Given:

f (x) = sin √2x

f (x + h) = sin √2(x+h)

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 38

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 39

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 40

(ii) cos √x

Given:

f (x) = cos √x

f (x + h) = cos √(x+h)

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 41

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 42

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 43

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