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Edited By Ramraj Saini | Updated on Dec 03, 2023 05:06 PM IST | #CBSE Class 12th

**NCERT Solutions for Exercise 5.5 Class 12 Maths Chapter 5 Continuity and Differentiability **are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the **latest syllabus and pattern of CBSE 2023-24. **In the previous exercise , you have already learned about the differentiation of logarithmic and exponential functions. In exercise 5.5 Class 12 Maths, you will learn about logarithmic differentiation which is not the same as differentiation of logarithmic functions. This trick of differentiation is used for the differentiation of functions raised to the power of functions or variables.

In **NCERT solutions for Class 12 Maths chapter 5 exercise 5.5**, you will learn that logarithmic differentiation relies on the property of log and chain rule that you have already learned. If you have a good command of the chain rule of differentiation, you can easily solve these problems even without knowing about the logarithmic differentiation. You can go through these Class 12th Maths chapter 5 exercise 5.5 to get in-depth knowledge of this concept. **12th class Maths exercise 5.5 **answers** **are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

**Also, see**

- Continuity and Differentiability Exercise 5.1
- Continuity and Differentiability Exercise 5.2
- Continuity and Differentiability Exercise 5.3
- Continuity and Differentiability Exercise 5.4
- Continuity and Differentiability Exercise 5.6
- Continuity and Differentiability Exercise 5.7
- Continuity and Differentiability Exercise 5.8
- Continuity and Differentiability Miscellaneous Exercise

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**Question:1 **Differentiate the functions w.r.t. x.

Given function is

Now, take log on both sides

Now, differentiation w.r.t. x

There, the answer is

Given function is

Take log on both the sides

Now, differentiation w.r.t. x is

Therefore, the answer is

Given function is

take log on both the sides

Now, differentiation w.r.t x is

Therefore, the answer is

Given function is

Let's take

take log on both the sides

Now, differentiation w.r.t x is

Similarly, take

Now, take log on both sides and differentiate w.r.t. x

Now,

Therefore, the answer is

Given function is

Take log on both sides

Now, differentiate w.r.t. x we get,

Therefore, the answer is

Given function is

Let's take

Now, take log on both sides

Now, differentiate w.r.t. x

we get,

Similarly, take

Now, take log on both sides

Now, differentiate w.r.t. x

We get,

Now,

Therefore, the answer is

Given function is

Let's take

Now, take log on both the sides

Now, differentiate w.r.t. x

we get,

Similarly, take

Now, take log on both sides

Now, differentiate w.r.t. x

We get,

Now,

Therefore, the answer is

Given function is

Lets take

Now, take log on both the sides

Now, differentiate w.r.t. x

we get,

Similarly, take

Now, differentiate w.r.t. x

We get,

Now,

Therefore, the answer is

Given function is

Now, take

Now, take log on both sides

Now, differentiate it w.r.t. x

we get,

Similarly, take

Now, take log on both the sides

Now, differentiate it w.r.t. x

we get,

Now,

Therefore, the answer is

Given function is

Take

Take log on both the sides

Now, differentiate w.r.t. x

we get,

Similarly,

take

Now. differentiate it w.r.t. x

we get,

Now,

Therefore, the answer is

Given function is

Let's take

Now, take log on both sides

Now, differentiate w.r.t. x

we get,

Similarly, take

Now, take log on both the sides

Now, differentiate w.r.t. x

we get,

Now,

Therefore, the answer is

Given function is

Now, take

take log on both sides

Now, differentiate w.r.t x

we get,

Similarly, take

Now, take log on both sides

Now, differentiate w.r.t. x

we get,

Now,

Therefore, the answer is

Given function is

Now, take

take log on both sides

Now, differentiate w.r.t x

we get,

Similarly, take

Now, take log on both sides

Now, differentiate w.r.t. x

we get,

Now,

Therefore, the answer is

Given function is

Now, take log on both the sides

Now, differentiate w.r.t x

By taking similar terms on the same side

We get,

Therefore, the answer is

Given function is

Now, take log on both the sides

Now, differentiate w.r.t x

By taking similar terms on same side

We get,

Therefore, the answer is

f ' (1)

Given function is

Take log on both sides

NOW, differentiate w.r.t. x

Therefore,

Now, the vale of is

(i) by using product rule

Given function is

Now, we need to differentiate using the product rule

Therefore, the answer is

(ii) by expanding the product to obtain a single polynomial.

Given function is

Multiply both to obtain a single higher degree polynomial

Now, differentiate w.r.t. x

we get,

Therefore, the answer is

(iii) by logarithmic differentiation.

Do they all give the same answer?

Given function is

Now, take log on both the sides

Now, differentiate w.r.t. x

we get,

Therefore, the answer is

And yes they all give the same answer

It is given that u, v and w are the functions of x

Let

Now, we differentiate using product rule w.r.t x

First, take

Now,

-(i)

Now, again by the product rule

Put this in equation (i)

we get,

Hence, by product rule we proved it

Now, by taking the log

Again take

Now, take log on both sides

Now, differentiate w.r.t. x

we get,

Hence, we proved it by taking the log

Class 12 Maths ch 5 ex 5.5 consists of questions related to finding differentiation of functions raised to the power of functions. These types of questions can be solved using the concept called logarithmic differentiation. In NCERT book exercise 5.5 Class 12 Maths which you learn this concept through solving problems based on this concept. There are 10 questions from this concept given in the exercise 5.5 class 12 maths. Also, you can solve two examples give before this exercise which will help you to get conceptual clarity. The proof of this concept is also given before this exercise. You can prove the given definition by yourself using the chain rule and logarithmic property.

**Also Read|** Continuity and Differentiability Class 12th Chapter 5 Notes

- NCERT Solutions for Class 12 Maths chapter 5 exercise 5.5 are beneficial when students are getting difficulty while solving the NCERT syllabus exercise 5.5 Class 12 Maths problems.
- Class 12 Maths chapter 5 exercise 5.5 solutions are descriptive so you can easily understand the solutions.
- Class 12th Maths chapter 5 exercise 5.5 solutions can be used for reference when you are solving logarithmic differentiation.

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Download EBook**Comprehensive Coverage:**The solutions encompass all the topics covered in ex 5.5 class 12, ensuring a thorough understanding of the concepts.**Step-by-Step Solutions:**In this class 12 maths ex 5.5, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.**Accuracy and Clarity:**Solutions for class 12 ex 5.5 are presented accurately and concisely, using simple language to help students grasp the concepts easily.**Conceptual Clarity:**In this 12th class maths exercise 5.5 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.**Inclusive Approach:**Solutions for ex 5.5 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.**Relevance to Curriculum:**The solutions for class 12 maths ex 5.5 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.

**Also see-**

- NCERT Solutions for Class 12 Maths
- NCERT Solutions for Class 12 Physics
- NCERT Solutions for Class 12 Chemistry
- NCERT Solutions for Class 12 Biology

- NCERT Exemplar Solutions for Class 12th Maths
- NCERT Exemplar Solutions for Class 12th Physics
- NCERT Exemplar Solutions for Class 12th Chemistry
- NCERT Exemplar Solutions for Class 12th Biology

**Happy learning!!!**

1. Does logarithmic differentiation and differentiation of logarithmic function is same ?

No, logarithmic differentiation and differentiation of logarithmic function are different concepts.

2. What is use of logarithmic differentiation ?

Logarithmic differentiation is useful for differentiating the function raised to the power of some variable or function.

3. What is weightage of Vector Algebra if the CBSE Class 12 Maths board exam ?

The weightage of Vector Algebra is 7 marks in the CBSE Class 12 Maths board exam. For good score follow NCERT book. To solve more problems NCERT exemplar and previous year papers can be used.

4. Can i get CBSE Class 12 Syllabus ?

Click on the link to get CBSE Class 12 Syllabus.

5. What is the application process for CBSE Class 12 ?

Click on the link to get application process for CBSE Class 12

6. What is the exam duration of CBSE Class 12 Maths ?

Total of 3 hours will be given to you to complete the CBSE Class 12 Maths paper.

7. What is the differentiation of e^(2x) ?

The differentiation of e^(2x) is 2 e^(2x).

8. Find the differentiation of 1/x ?

d(1/x)/dx = -1/x^2

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6 minHave a question related to CBSE Class 12th ?

You can use them people also used problem

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

Hello Akash,

If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.

You can get the Previous Year Questions (PYQs) on the official website of the respective board.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

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Thank you and wishing you all the best for your bright future.
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Hello student,

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If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:
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- No school admission needed! Register directly with CBSE. (But if you want to attend the school then you can take admission in any private school of your choice but it will be waste of money)
- You have to appear for the 2025 12th board exams.
- Registration for class 12th board exam starts around September 2024 (check CBSE website for exact dates).
- Aim to register before late October to avoid extra fees.
- Schools might not offer classes for private students, so focus on self-study or coaching.

**
Remember
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, these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.

I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.

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