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RD Sharma is considered the best material for CBSE students. They are used all over the country and are extremely helpful for exam preparation. They are preferred over NCERT due to their syllabus coverage and detail of answers.

RD Sharma Class 12th Exercise 10.4 deals with the chapter ' Differentiation.' This is a fundamental chapter with its applications across many subjects. This is why students need to familiarise themselves with the basics of this chapter.

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

- Chapter 10 -Differentiation - Ex-10.1
- Chapter 10 -Differentiation - Ex-10.2
- Chapter 10 -Differentiation - Ex-10.3
- 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 10.4 question 1

Answer:

Hint:

Use product rule to find

Given:

Solution:

Differentiate the given equation w.r.t x

Hence is the required answer.

Differentiation exercise 10.4 question 2

Answer:Hint:

Use product rule to find

Given:

Solution:

Differentiating the given equation w.r.t x

Is the required answer.

Hence

Hint:

Use the differentiation formula of

i.e.

Given:

Solution:

Differentiate the given equation w.r.t x

Hence is required answer

Differentiation exercise 10.4 question 4

Answer:Hint:

Use chain rule to find the differentiation

Given:

Solution:

Differentiate the given equation w.r.t x

[Using the chain ]

Hence

Is the required answer

Differentiation exercise 10.4 question 5

Answer:Hint:

Use chain rule and differentiation formulas like

Given:

Solution:

Differentiate the given equation w.r.t x

Hence is the required answer

Differentiation exercise 10.4 question 6

Answer:Hint:

Use chain rule to find the differentiation formula like

Given:

Solution:

Differentiate the given equation w.r.t x

Hence is the required answer

Differentiation exercise 10.4 question 7

Answer:Hint:

Use chain rule and product rule

Given:

Solution:

Differentiate the given equation w.r.t x

Hence is the required answer

Differentiation exercise 10.4 question 8

Answer:Hint:

Use chain rule and the product rule of differentiation

Given:

Solution:

Differentiate the given equation w.r.t x

[Product Rule ]

Hence is the required answer.

Differentiation exercise 10.4 question 9

Answer:Hint:

Use chain rule and

Given:

Solution:

Differentiate the given equation w.r.t x

[Using chain rule]

Hence is the required answer

Differentiation exercise 10.4 question 10

Hint:

Use chain rule and quotient rule

Given:

Solution:

Differentiate the given equation w.r.t x

[Using quotient rule ]

Hence is the required differentiation.

Differentiation exercise 10.4 question 11

Answer:Hint:

Use chain rule and product rule

Given:

Solution:

Differentiate the given equation w.r.t x

[Using chain rule]

Hence, is the required answer.

Differentiation exercise 10.4 question 12

Answer:

Hint:

Use to formulas and use

Given:

Solution:

Let

So, the equation will become

Differentiate the above equation w.r.t x

Hence, if

Then, is the required answer

Hence proved

Differentiation exercise 10.4 question 13

Answer:Hint:

Use trigonometric identities and differentiation formula of inverse trigonometric functions

Given:

Solution:

Let

The given equation becomes

Differentiate w.r.t x

Hence if

Then, Is the required answer

Differentiation exercise 10.4 question 14

Answer:Hint:

Use product rule

Given:

Solution:

Differentiate w.r.t x

Hence, if

Then hence proved

Differentiation exercise 10.4 question 15

Answer:Hint:

Use product rule and

Given:

Solution:

Differentiate w.r.t x

[Product rule ]

Hence, if then is the required answer

Hence proved

Differentiation exercise 10.4 question 16

Answer:Hint:

Use quotient rule and algebraic identities

Given:

Solution:

Squaring both the side,

Differentiate this above equation w.r.t x

[Using quotient rule]

Hence proved

Differentiation exercise 10.4 question 17

Answer:Hint:

Use quotient rule and properties of logarithm

Given:

Solution:

Differentiate this above equation w.r.t x

Hence proved

Differentiation exercise 10.4 question 18

Answer:Hint:

Use quotient rule

Given:

Solution:

Differentiating w.r.t x

[Use quotient rule]

Thus, proved

Differentiation exercise 10.4 question 19

Hint:

Use differentiation formulas

Given:

Solution:

Differentiate the given equation w.r.t x

Thus, proved

Differentiation exercise 10.4 question 20

Answer:Hint:

Use product rule and chain rule

Given:

Solution:

Differentiate the given equation w.r.t x

[Use product rule and chain rule]

Also

Put in the above equation

Thus, proved

Differentiation exercise 10.4 question 21

Hint:

Use chain rule

Given:

Solution:

Differentiate the given equation w.r.t x

[Using chain rule]

Put in the above equation

Thus, proved

Differentiation exercise 10.4 question 22

Answer:Hint:

Use chain rule

Given:

Solution:

Differentiating equation w.r.t x

[Use chain rule]

Thus, proved

Differentiation exercise 10.4 question 23

Answer:Hint:

Use product rule and chain rule

Given:

Solution:

Differentiate w.r.t x

[Using product rule]

[Using chain rule]

Thus, proved

Differentiation exercise 10.4 question 24

Answer:Hint:

Use product rule and chain rule

Given:

Solution:

Differentiate w.r.t x

[Use product rule and chain rule]

Thus, proved

Differentiation exercise 10.4 question 25

Answer:Hint:

Use chain rule and

Given:

Solution:

Differentiate w.r.t x

[Using chain rule and ]

Hence proved

Differentiation exercise 10.4 question 26

Answer:Hint:

Use chain rule

Given:

Solution:

Differentiate w.r.t x

[Using chain rule and ]

Differentiation exercise 10.4 question 27

Answer:Hint:

Use chain rule

Given:

Solution:

Differentiate w.r.t x

[Using chain rule]

Thus proved

Differentiation exercise 10.4 question 28

Answer:Hint:

Use chain rule and product rule

Given:

Solution:

Differentiate the given equation w.r.t x

[Use chain rule and product rule]

Also

Put this values of x in the above equation

Thus, proved

Differentiation exercise 10.4 question 29

Hint:

Use chain rule and product rule

Given:

Solution:

Differentiate the given equation w.r.t x

[Using chain rule]

[Using product rule]

At

Hence at

Differentiation exercise 10.4 question 30

Answer:Hint:

Use chain rule and differentiation of inverse trigonometric function

Given:

Solution:

Differentiate w.r.t x

[Using chain rule]

Put

At

Hint:

Use chain rule

Given:

Solution:

Differentiate the given equation w.r.t x

[Using chain rule]

Rationalizing the denominator

Thus proved

RD Sharma Class 12th Exercise 10.4 has a total of 31 questions including subparts, that are divided into two levels. Level 1 sums are less complex and can be solved using the fundamentals. In contrast, Level 2 sums are lengthy and require additional knowledge. Therefore, students should divide their work and study accordingly because they cannot cover the entire topic in one go.

The Level 1 questions in example 10.4 cover topics like finding dy/dx of quadratic and trigonometric equations, prove that sums, evaluation sums, etc. Level 2, On the other hand, contains questions mainly consisting of finding dy/dx at given parameters.

As Differentiation is a vast chapter, students should study efficiently to cover all topics within the stipulated time. Otherwise, it gets very strenuous to complete at the last moment. As RD Sharma's books are pretty extensive, solving all the problems is not an option. Instead, students should refer to this material to quickly gain an understanding of the concepts.

As RD Sharma Class 12th Exercise 10.4 material contains all the solutions in one place, it is very easy for revision. Teachers won't be able to cover hundreds of problems in their lectures. Students can compare their progress and stay on top of their Class with the help of RD Sharma Class 12 Chapter 10 Exercise 10.4 solutions.

After the introduction of such precise solved materials, The traditional textbook reference method is long gone. Instead, it has been found that students understand topics even better and can study efficiently with the help of solved materials. These materials are the key to scoring good marks, which is why students should start preparing from these sources without wasting any time.

As there are different ways towards solving a problem in Differentiation, students can find the easiest of them and solve accordingly with the help of this material. These expert-created solutions are updated to the latest version of the book, which means there would be no missing questions or additional questions. Moreover, the answers are provided by Brainly to help students in their exam preparation. This is why RD Sharma Class 12th Exercise 10.4 is free and accessible through their website. This means that you can access them anywhere, anytime, with an internet connection.

- 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. What is the benefit of this material from an exam standpoint?

Class 12 RD Sharma Chapter 10 Exercise 10.4 Solution material has solutions that cover all important topics and are essential for exam preparation.

2. Do we have to pay any hidden charges?

No, RD Sharma Class 12 solutions Differentiation Ex 10.4 material is provided by Brainly free of cost for students to study hassle-free.

3. What is differentiation?

Differentiation is the process of finding derivatives of a function that helps determine its rate of change.

4. What are the applications of differentiation?

Differentiation and the maxima and minima concept is widely used in economics and finding the rate of growth of businesses. You can refer to RD Sharma Class 12 Solutions Chapter 10 Ex 10.4 to learn more about this topic.

5. Can I score good marks in exams through this material?

RD Sharma Class 12th Exercise 10.4 material will help students get a better understanding of the chapter and score gold marks in exams.

Mar 22, 2023

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