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Edited By Satyajeet Kumar | Updated on Jan 20, 2022 05:16 PM IST

RD Sharma Class 12th Exercise 10.2 is very important because RD Sharma has always been the best book for every student. RD Sharma Mathematics has set a standard where all the essential concepts and theorems are mentioned to become the teacher's favorite. Moreover, the questions in board exams and competitive exams have come from RD Sharma's book for many years.

Rd Sharma Class 12th Exercise 10.2 has solved every problem of a student regarding differentiation. Differentiation Ex. 10.2 Solutions has 76 questions including subparts, that are formatted in a way that students will enjoy doing them. The exercise includes differentiating the functions w.r.t. to x, recapitulation of the product rule, quotient rule differentiation of the constant, differentiation of inverse trigonometric functions, logarithmic differentiation, etc.

**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 10 -Differentiation - Ex-10.1
- Chapter 10 -Differentiation - Ex-10.3
- Chapter 10 -Differentiation - Ex-10.4
- Chapter 10 -Differentiation - Ex-10.5
- Chapter 10 -Differentiation - Ex-10.6
- Chapter 10 -Differentiation - Ex-10.7
- Chapter 10 -Differentiation - Ex-10.8
- Chapter 10 -Differentiation - Ex-FBQ
- Chapter 10 -Differentiation - Ex-MCQ
- Chapter 10 -Differentiation - Ex-VSA

Differentiation exercise 10.2 question 1

Answer:

Hint: You must know the values of solving derivative problems.Given:

Solution:

Let :

Differentiating with respect to x,

[using chain rule]

So,

Differentiation exercise 10.2 question 2

Answer:Hint: You must know the rules of solving derivative of trigonometric functions.

Given:

Solution:

Let

Differentiating with respect to x,

So, [ using chain rule]

Differentiation exercise 10.2 question 3

Answer:Hint: You must know the rules of solving derivative of trigonometric function.

Given:

Solution:

...To convert degree into radian multiply by

Differentiating with respect to x,

[ using chain rule]

.

Differentiation exercise 10.2 question 4

Answer:Hint: You must know the rules of solving derivative of logarithm function.

Given:

Solution:

Differentiating with respect to x,

[ using chain rule]

Differentiation exercise 10.2 question 5

Answer:Hint: You must know the rules of solving derivation of exponential function and trigonometric function.

Given:

Solution:

Let

Differentiating with respect to x,

[using chain rule]

[again using chain rule]

Differentiation exercise 10.2 question 6

Answer:Hint:You must know the rules of solving derivation of exponential function and trigonometric function.

Given:

Solution:

Differentiating with respect to x,

[ using chain rule] and

Differentiation exercise 10.2 question 7

Answer:Hint: You must know the rules of solving derivation of trigonometric function.

Given:

Solution:

Let

Differentiating with respect to x,

[ using chain rule ]

.

Differentiation exercise 10.2 question 8

Answer:Hint: You must know the rules of solving derivative of logarithm function.

Given:

Solution:

Let

Differentiating with respect to x,

[ using chain rule ]

Differentiation exercise 10.2 question 9

Answer:Hint: You must know the rules of solving derivative of logarithm function.

Given:

Solution:

Let or

Differentiating with respect to x

[ using chain rule ]

Differentiation exercise 10.2 question 10

Answer:Hint: You must know the rules of solving derivative of polynomial function.

Given:

Solution:

Let

Differentiating with respect to x

[using chain rule]

Differentiation exercise 10.2 question 11

Answer:Hint: You must know the rules of solving derivative of exponential function.

Given:

Solution:

Let

Differentiating with respect to x

[ using chain rule]

Differentiation exercise 10.2 question 12

Answer:Hint: You must know the rules of solving derivative of logarithm function

Given:

Solution:

Let

Differentiating with respect to x

[ using chain rule]

Differentiation exercise 10.2 question 13

Answer:Hint: You must know the rules of solving derivative of polynomial function

Given:

Solution:

Let

Differentiating with respect to x

[using chain rule]

Differentiation exercise 10.2 question 14

Answer:Hint: You must know the rules of solving derivative of polynomial function

Given:

Solution:

Let

Differentiating with respect to x

Differentiation exercise 10.2 question 15

Answer:Hint: You must know the rules of solving derivative of logarithm and polynomial function.

Given:

Solution:

Let

Differentiating with respect to x

Differentiation exercise 10.2 question 16

Answer:Hint: You must know the rules of solving derivative of trigonometric function.

Given:

Solution:

Let

Differentiating with respect to x

Differentiation exercise 10.2 question 17

Answer:Hint: You must know the rules of solving derivative of polynomial function

Given:

Solution:

Let

Differentiating with respect to x

[ using chain rule]

Differentiation exercise 10.2 question 18

Answer:Hint: You must know the value of solving logarithm and trigonometric function.

Given:

Solution:

Let

Differentiating with respect to x

Differentiation exercise 10.2 question 19

Answer:Hint: You must know the rule of solving derivative of polynomial function.

Given:

Solution:

Let

Differentiating with respect to x

[ using chain rule]

Differentiation exercise 10.2 question 20

Answer:Hint: You must know the rules of solving derivative of trigonometric functions.

Given:

Solution:

Let

Differentiating with respect to x

[ using chain rule]

Differentiation exercise 10.2 question 21

Answer:Hint: You must know the rules of solving exponential and trigonometric functions.

Given:

Solution:

Let

Differentiating with respect to x

Differentiation exercise 10.2 question 22

Answer:Hint: You must know the rules of solving derivative of trigonometric and logarithm function.

Given:

Solution:

Let

Differentiating with respect to x

Using chain rule

Differentiation exercise 10.2 question 23

Answer:Hint: You must know the rules of solving derivative of exponential and trigonometric

Given:

Solution:

Let

Differentiating with respect to x

Differentiation exercise 10.2 question 24

Answer:Hint: You must know the rules of solving derivative of trigonometric and exponential function.

Given:

Solution:

Let

Differentiate both sides

Using Chain Rule,

Differentiation exercise 10.2 question 25

Answer:

Hint: You must know the rules of solving derivative of logarithm trigonometric function.Given:

Solution:

Let

Differentiating with respect to x

Differentiation exercise 10.2 question 26

Answer:Hint: You must know the rules of solving derivative of logarithm and trigonometric function.

Given:

Solution:

Let

using

Differentiate with respect to x

Using quotient rule

Differentiation exercise 10.2 question 27

Answer:Hint: You must know the rules of solving derivative of exponential and trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 28

Answer:Hint: You must know the rules of solving derivative of logarithm function.

Given:

Solution:

Differentiate with respect to x

Differentiation exercise 10.2 question 29

Answer:Hint: You must know about the rules of solving derivative of exponential and logarithm functions.

Given:

Solution:

Let

Differentiate with respect to x,

[using quotient rule]

Differentiation exercise 10.2 question 30

Answer:Hint: You must know the rules of solving derivation of logarithm and trigonometric function.

Given:

Solution:

Let

Differentiate both sides,

Differentiation exercise 10.2 question 31

Answer:Hint: You must know the rules of solving derivative of exponential function.

Given:

Solution:

Let

Differentiate with respect to x,

Using quotient rule,

Differentiation exercise 10.2 question 32

Answer:Hint: You must know about the rules of solving derivative of logarithm functions.

Given:

Solution:

Let

Differentiate with respect to x,

Now apply quotient rule,

Differentiation exercise 10.2 question 33

Answer:Hint: You must know about the rules of solving derivative of Inverse trigonometric function and exponential

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 34

Answer:Hint: You must know about the rules of solving derivative of Inverse trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 35

Answer:Hint: You must know about the rules of solving derivative of Trigonometry and Inverse trigonometric function

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 36

Answer:Hint: You must know about the rules of solving derivative of Exponential and Inverse trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 37

Answer:Hint: You must know about the rules of solving derivative of Inverse trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 38

Answer:Hint: You must know about the rules of solving derivative of logarithm and Inverse trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 39

Answer:Hint: You must know about the rules of solving derivative of trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 40

Answer:Hint: You must know about the rules of solving derivative of trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 41

Answer:Hint: You must know about the rules of solving derivative of logarithm function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 42

Answer:Hint: You must know about the rules of solving derivative of trigonometric function.

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 43

Answer:Hint: you must know the rules of solving derivative of trigonometric and logarithm function,

Given:

Solution:

Let

Differentiate with respect to x,

Differentiation exercise 10.2 question 44

Answer:Hint: you must know about the rules of solving derivative of exponential logarithm and trigon function

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 45

Hint: you must know the rules of solving derivative of polynomials

Given:

Solution:

Let

By rationalizing,

Now, let

Now, differentiate

Differentiation exercise 10.2 question 46

Answer:Hint: you must know the rules of solving derivative of logarithm function

Given:

Solution:

Let

Differentiate both side with respect to x

Differentiation exercise 10.2 question 47

Answer:Hint: you must know the rules of solving derivative of inverse trigonometric function

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 48

Answer:Hint: you must know the rules of solving derivative of inverse trigonometric function

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 49

Answer:Hint: you must know the rules of solving exponential derivative

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 50

Answer:Hint: you must know the rule of solving exponential and logarithm functions

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 51

Answer:Hint: you must know the rule of solving derivative of trigonometric function

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 52

Answer:Hint: you must know the rule of solving derivative of trigonometric functions

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 53

Answer:Hint: you must know the rule of solving derivative of logarithm and trigonometric functions

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 54

Answer:Hint: you must know the rule of solving derivative of exponential and trigonometric functions

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 55

Answer:Hint: you must know the rule of solving derivative of logarithm and trigonometric functions

Given:

Solution:

Let

Differentiate with respect to x

[ Using chain rule ]

Differentiation exercise 10.2 question 56

Hint: you must know the rule of solving derivative of logarithm and trigonometric functions

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 57

Answer:Hint: you must know the rule of solving derivative of logarithm functions

Given:

Solution:

Let

Differentiate with respect to x

Differentiation exercise 10.2 question 58

Answer: ProvedHint: you must know the rule of solving derivative of logarithm functions

Given:

Solution:

Let

Differentiate with respect to x

∴ Proved

Differentiation exercise 10.2 question 59

Answer: ProvedHint: you must know the rule of solving derivation of functions

Given:

Prove :

Solution:

Let

Differentiate with respect to x

∴ Proved

Differentiation exercise 10.2 question 60

Answer: ProvedHint: you must know the rule of solving derivation of functions.

Given:

Prove :

Solution:

Let

Differentiate with respect to x and apply quotient rule

∴ Proved

Differentiation exercise 10.2 question 61

Answer: ProvedHint: you must know the rule of solving logarithm functions.

Given:

Prove

Solution:

Let

Differentiate with respect to x

∴ Proved

Differentiation exercise 10.2 question 62

Answer: ProvedHint:: you must know the rules of solving derivation of logarithm functions.

Given:

Prove

Solution:

Let

Differentiate with respect to x,

∴ Proved

Differentiation exercise 10.2 question 63

Answer: ProvedHint: you must know the rule of solving derivation of functions.

Given:

Prove

Solution:

Let

Differentiate with respect to x,

Proved

Differentiation exercise 10.2 question 64

Answer: ProvedHint: you must know the rules of derivative of inverse trigonometric functions.

Given:

Prove

Solution:

Let

Differentiate with respect to x,

[ quotient rule ]

Where

∴ Proved

Differentiation exercise 10.2 question 65

Answer: ProvedHint: you must know the rules of derivative of exponential functions.

Given:

Prove

Solution:

Let

Differentiate with respect to x,use quotient rule

∴ Proved

Differentiation exercise 10.2 question 66

Answer: ProvedHint: you must know the rules of derivative of logarithm functions.

Given:

Prove:

Solution:

Let

Differentiate with respect to x, use product rule

[ use product rule]

∴ Proved

Differentiation exercise 10.2 question 67

Answer:ProvedHint: you must know the rules of derivative of exponential and trigonometric functions.

Given:

Prove:

Solution:

Let

Differentiate with respect to x,use product rule

Multiply and divide by

∴ Proved

Differentiation exercise 10.2 question 68

Answer:ProvedHint: you must know the rules of derivative of logarithm and trigonometric functions.

Given:

Prove:

Solution:

Differentiate with respect to x,use chain rule

Multiply and divide by 2

∴ Proved

Differentiation exercise 10.2 question 69

Answer: ProvedHint: you must know the rules of solving derivative of inverse trigonometric functions.

Given:

Prove:

Solution:

Differentiate with respect to x,use product rule

∴ Proved

Differentiation exercise 10.2 question 70

Answer:ProvedHint: you must know the rules of solving derivatives.

Given:

Prove:

Solution:

Squaring both sides,

Differentiate both sides,

∴ Proved

Differentiation exercise 10.2 question 71

Answer:ProvedHint: you must know the rules of solving derivatives of exponential functions.

Given:

Prove:

Solution:

Differentiate with respect to x,

∴ Proved

Differentiation exercise 10.2 question 72

Answer:ProvedHint: you must know the rules of solving derivatives.

Given:

Prove:

Solution:

Squaring both sides,

Differentiate with respect to x,

∴ Proved

Differentiation exercise 10.2 question 73

Answer:ProvedHint: you must know the rules of solving derivatives.

Given:

Prove:

Solution:

Differentiate with respect to x,

( multiplying by 4 in num. & den.)

Dividing both sides with x,

∴ Proved

Differentiation exercise 10.2 question 74

Answer:ProvedHint: you must know the rules of solving derivatives.

Given: Prove that

Solution:

∴ Proved

Differentiation exercise 10.2 question 75

Answer:Hint: you must know the rules of solving derivatives of trigonometric function

Given:

Find :

Solution:

Now rationalize

Differentiate with respect to x,

Differentiation exercise 10.2 question 76

Answer:Hint: you must know the rules of solving derivative of trigonometric functions

Given:

Find:

Solution:

Differentiate with respect to x,

Now,

Rd Sharma Class 12th Exercise 10.2 solutions will help every student, and they will be able to clear the concepts and learn according to an exam point of view. The benefits of these solutions are:

**Created by experts**

Rd Sharma Class 12th Exercise 10.2 solutions are created not by a single person but by a team. The team discusses every question in detail and then provides it to the student. Therefore, a student will never face any difficulty in mathematics after going for Rd Sharma Class 12th Chapter 10.2 Exercise 10.2 solutions.

**Best Solutions for preparation**

Rd Sharma Class 12th Exercise 10.2 solutions help students to prepare better for exams as every concept is cleared in a precise manner. The students will be ready to face any exam with Class 12th RD Sharma Chapter 10.2 Exercise 10.2 Solutions.

**NCERT based questions**

The solutions help a student do the homework quite easily and effectively as these solutions are primarily based on NCERT questions. In addition, these solutions make every student an expert in solving these questions.

**Different ways to solve a question**

RD Sharma Class 12 Solutions Chapter 10 ex 10.2 helps students find alternative ways to solve a question. The concepts are interconnected and solved by experts that a student finds it easy to understand and solve questions in a different manner.

**Benchmark performance**

The solutions help a student perform well in exams. RD Sharma Class 12 Solutions Differentiation Ex. 10.2 covers all the important questions that usually come in exams, which helps the student set a benchmark score in exams.

**Free of cost**

Students will find all these solutions free of cost at Career360, the best site to grab the benefits and score well with flying colors. At Career360, a student will understand, learn and perform exceptionally in exams. Thousands of students have benefitted from these solutions, and now it is your turn to shine.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Are these solutions enough to prepare for board and competitive exams?

Yes, these solutions cover every concept, and a student will learn these concepts quickly and in different ways; these solutions are enough.

2. Why should I refer to these solutions?

These solutions will make every student shine in exams as understanding and learning have become easy. Every question is created by a team of experts who take utmost care to make the solutions perfect.

3. Are these solutions free?

Yes, these solutions are free of cost at Career360, and anyone can download them and grab the benefits.

4. What is differentiation?

The instant rate of change in the function based on one of the two variables is called differentiation in mathematics.

5. What are some examples of differentiation?

Velocity equal to the rate of change of displacement to time, acceleration equal to the rate of change of velocity to time are some examples of differentiation.

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