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Edited By Satyajeet Kumar | Updated on Jan 20, 2022 05:35 PM IST

RD Sharma books are well known for their accuracy, subject knowledge and exam-oriented questions. There is always a high possibility that the questions in CBSE exams might appear from this book as many schools refer to them for setting up question papers.**RD Sharma Class 12th Exercise 10.5** Is designed specifically for students to prepare for exams. It is created by a team of subject experts that have years of experience with exam-oriented materials. These solutions will help students get a better understanding of the subject and score good marks in exams.

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**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-10.4
- 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

Taking log on both sides,

Differentiate both sides,

[using product rule]

put value of

Differentiation exercise 10.5 question 2

Take natural log to both sides

Diff both side w.r.t

Using implicit diff on LHS, product rule on RHS

Substituting back for y

Differentiation exercise 10.5 question 3

Taking log on both the sides,

Differentiating with respect to ,

[Using product rule]

[Using equation (i)]

Differentiate w.r.t

Differentiation exercise 10.5 question 5

Taking log both sides

Differentiate w.r.t ,

Now, put value of

Differentiation exercise 10.5 question 6

Taking log both sides

Differentiate w.r.t

Using product of rule

Differentiation exercise 10.5 question 7

Taking log both sides

Differentiate w.r.t x,

Differentiation exercise 10.5 question 8

Taking log on both sides

Differentiate w.r.t x,

[ use multiplication rule]

Differentiation exercise 10.5 question 9

Let ........(i)

taking log on both sides,

Differentiate w.r.t x, using product rule and chain rule,

[Using equaton (i)]

Differentiation exercise 10.5 question 10

Taking log both sides

Differentiate w.r.t x,

......[Using (1)]

Differentiation exercise 10.5 question 11

**Answer: **

Taking log on both sides

Differentiate w.r.t x,

Use product rule

Differentiation exercise 10.5 question 12

Taking log on both sides

Differentiate w.r.t x,

Differentiation exercise 10.5 question 13

Taking log on both sides

Differentiation exercise 10.5 question 14

Taking log on both sides

Differentiate w.r.t x,

Now , put the value of ,

Differentiation exercise 10.5 question 15

Taking log on both sides

Differentiation exercise 10.5 question 16

Taking log on both sides

So,

Differentiate w.r.t x,

Differentiation exercise 10.5 question 17

Taking log on both sides

Differentiation exercise 10.5 question 18 (i)

Let,

Taking log both side

Differentiation exercise 10.5 question 18 (ii)

.........(1)

Take log

Using (1) we get

Differentiation exercise 10.5 question 18 (iii)

Diff by w.r.t.x

Calculate

Take log on both sides

Diff w.r.t x

Use product rule

Where

Calculate

Diff w.r.t x

Use quotient rule

Now

Put value

Differentiation exercise 10.5 question 18 (iv)

Take log both sides

.....................(1)

Take log both side

............(2)

From (1) and (2)

Differentiation exercise 10.5 question 18 (v)

Diff w.r.t x

Calculate

Take log on both side

Use product rule

Calculate

Taking

Diff w.r.t. x

Use product rule

Now

Put value of

Differentiation exercise 10.5 question 18 (vi)

Let

Take log on both sides

Diff w.r.t x

Thus

Differentiation exercise 10.5 question 18 (viii)

Now

Take log on both sides

Differentiation exercise 10.5 question 19

Let

..........(1)

For

Put in eq (1)

0

Differentiation exercise 10.5 question 20

As we know

According to question

.......(1)

Take

Put in eq. (1)

Differentiation exercise 10.5 question 21

Taking log on both sides,

w.r.t x

Differentiation exercise 10.5 question 22

Taking log on both sides,

Differentiation exercise 10.5 question 23

Diff w.r.t x

Differentiation exercise 10.5 question 24

Taking log on both sides,

Differentiation exercise 10.5 question 27

Let's assume

.......(1)

Now

On diff both sides w.r.t. x

.......(2)

On diff both sides w.r.t. x

........(3)

Diff w.r.t x

.......(1)

Taking log on both sides

.......(2)

.........(3)

Put (2) and (3) in eq(1)

Differentiation exercise 10.5 question 28 (ii)

**Answer: ****Hint: ** Differentiate the equation taking log on both sides**Given: ****Solution: **

Diff w.r.t x

.......(1)

On diff both side with respect to x we get

from 1

........(3)

Put (2) and (3) in eq(1)

Differentiation exercise 10.5 question 29 (i)

Differentiation exercise 10.5 question 29 (ii)

.............(1)

Diff w.r.t x

..............(2)

Diff w.r.t x

...........(3)

Put (2) and (3) in eq (1)

Let

Differentiation exercise 10.5 question 31

**Answer: ****Hint: **Differentiate the equation taking log on both sides**Given: ****Solution: **

Let

Let

Differentiation exercise 10.5 question 32

Let’s assume

Now

Diff w.r.t x

.............(1)

Diff both sides w.r.t x

...............(2)

Hence proved

Differentiation exercise 10.5 question 34

Taking log on both sides,

Differentiation exercise 10.5 question 35

Let take

Put the value of we get

Taking log on both sides,

on diff. we get

Taking log both side

on diff. we get

Hence

Differentiation exercise 10.5 question 37

Taking log on both sides,

Taking log on both sides,

Differentiation exercise 10.5 question 39

Differentiation exercise 10.5 question 40

Differentiation exercise 10.5 question 41

Hence it is proved

Differentiation exercise 10.5 question 42

Taking log on both sides,

Differentiation exercise 10.5 question 43

Diff w.r.t x

Hence proved

Differentiation exercise 10.5 question 44

...................(1)

Hence proved

Differentiation exercise 10.5 question 45

Hence proved

Differentiation exercise 10.5 question 46

Hence proved

Differentiation exercise 10.5 question 47

Hence proved

Hence proved

Differentiation exercise 10.5 question 49

Hence proved

Differentiation exercise 10.5 question 50

Hence proved

Differentiation exercise 10.5 question 51

Differentiation exercise 10.5 question 52

Differentiation exercise 10.5 question 53

Taking log on both sides,

Differentiation exercise 10.5 question 54

Diff w.r.t

Diff w.r.t. x

...........(1)

Taking log on both sides,

Diff w.r.t. u

..............(2)

Taking log on both sides,

Diff w.r.t

..........(3)

Log on b.s.

Diff w.r.t

From (1)

Differentiation exercise 10.5 question 56

Taking log on both sides,

..........(1)

Differentiation exercise 10.5 question 57

Hence proved

Taking log on both sides,

Differentiate w.r.t x we get

Hence proved

Differentiation exercise 10.5 question 59

Diff w.r.t x we get

[Chain rule]

Differentiation exercise 10.5 question 60

Differentiation exercise 10.5 question 61

.............(1)

.................(2)

Differentiation exercise 10.5 question 62

Taking log on both side

............(1)

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 62

Edit Q

RD Sharma Class 12th Exercise 10.5 deals with the Chapter Differentiation and is a lengthy exercise consisting of 71 questions. As solving all of them at once is a tedious task, students should divide the sums and practice accordingly. Although these are basic level one questions they can be quite tricky unless students know their basics right.

In this exercise you will learn topics like:

1. Differentiation of Trigonometric equations

2. Differentiation involving exponents

3. Finding first derivatives of complex Algebraic equations

4. Proof sums involving derivatives

These are the following traits that make RD Sharma Class 12th Exercise 10.5 material the best choice for students:

1. **Detailed questions**

The solutions provided by Brinley contain detailed questions that cover the entire syllabus. This means that students don't have to worry about any missing topics.

**2. Step-by-step solutions**

These solutions are interpreted with step-by-step explanations that are extremely helpful for students to understand the questions properly. Students who find RD Sharma material confusing can refer to these solutions for a clear understanding. Class 12 RD Sharma Chapter 10 Exercise 10.5 Solution material is made in such a way that it is easy for both a class topper as well as an average student to study effectively.

3. **Helpful for class lectures**

As differentiation is a vast topic it is not necessary that teachers might cover all the questions from the book. This is why RD Sharma class 12 Chapter 10 Exercise 10.5 material is helpful for students to stay in line with their class lectures and side-by-side prepare for their exams.

4.** Exam-oriented material**

The sole purpose of this material is to enable students to score good marks in exams by merging all the solutions and concepts in a singular material. The questions from RD Sharma class 12 Chapter 10 Exercise 10.5 material are exam-oriented and as RD Sharma books are widely used the questions from this material can also show up in your exam.

- 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 are the charges for this material?

RD Sharma Class 12th Exercise 10.5 solutions are provided on Careers360’s website and are accessible for free. Students can refer to this material through their browser on the go without any hassle.

2. Which material is best suited for maths, RD Sharma or NCERT?

When compared to NCERT RD Sharma materials are exam oriented and best suited for maths. They contain detailed concepts with step-by-step explanations that help students better understand the subject.

3. Can I find solutions for all chapters on the Careers360’s website?

Students can search their relevant chapter name on Branly’s website to get access to their materials. To find solutions for Differentiation, refer to RD Sharma Class 12th Exercise 10.5.

4. What is differentiation?

The process of finding the rate of change of a function is called Differentiation. To learn more, check RD Sharma Class 12 solutions Differentiation Ex 10.5.

5. What are the real life applications of differentiation?

Given below are some of the applications:

Business and Economics

Distance and Velocity calculation

Variation in Temperature

Physics etc.

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