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NCERT Solutions for Exercise 5.2 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 NCERT syllabus Class 11 Maths, you have already learned about the derivatives of real value functions. Differentiation is defined as the process of finding the derivative of a function. In this article, you will get NCERT solutions for Class 12 Maths chapter 5 Exercise 5.2. This NCERT book exercise consists of questions related to finding derivatives of different types of functions.
Mainly derivatives of composite functions using chain rule are covered in the Class 12 Maths ch 5 ex 5.2. The chain rule is a very important concept to find the derivative of a composite function of two differentiable functions using derivatives of these functions. Solve problems from exercise 5.2 Class 12 Maths to get an understanding of the chain rule. Also, you can try to prove this theorem to get conceptual clarity. 12th class Maths exercise 5.2 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
Question:1.Differentiate the functions with respect to x in
Answer:
Given function is
when we differentiate it w.r.t. x.
Lets take . then,
(By chain rule)
Now,
Therefore, the answer is
Question:2. Differentiate the functions with respect to x in
Answer:
Given function is
Lets take then,
( By chain rule)
Now,
Therefore, the answer is
Question:3. Differentiate the functions with respect to x in
Answer:
Given function is
when we differentiate it w.r.t. x.
Lets take . then,
(By chain rule)
Now,
Therefore, the answer is
Question:4. Differentiate the functions with respect to x in
Answer:
Given function is
when we differentiate it w.r.t. x.
Lets take . then,
take . then,
(By chain rule)
Now,
Therefore, the answer is
Question:5. Differentiate the functions with respect to x in
Answer:
Given function is
We know that,
and
Lets take
Then,
(By chain rule)
-(i)
Similarly,
-(ii)
Now, put (i) and (ii) in
Therefore, the answer is
Question:6. Differentiate the functions with respect to x in
Answer:
Given function is
Differentitation w.r.t. x is
Lets take
Our functions become,
and
Now,
( By chain rule)
-(i)
Similarly,
-(ii)
Put (i) and (ii) in
Therefore, the answer is
Question:7. Differentiate the functions with respect to x in
Answer:
Give function is
Let's take
Now, take
Differentiation w.r.t. x
-(By chain rule)
So,
( Multiply and divide by and multiply and divide by )
There, the answer is
Question:8 Differentiate the functions with respect to x in
Answer:
Let us assume :
Differentiating y with respect to x, we get :
or
or
Question:9. Prove that the function f given by is not differentiable at x = 1.
Answer:
Given function is
We know that any function is differentiable when both
and are finite and equal
Required condition for function to be differential at x = 1 is
Now, Left-hand limit of a function at x = 1 is
Right-hand limit of a function at x = 1 is
Now, it is clear that
R.H.L. at x= 1 L.H.L. at x= 1
Therefore, function is not differentiable at x = 1
Question:10. Prove that the greatest integer function defined by is not differentiable at
x = 1 and x = 2.
Answer:
Given function is
We know that any function is differentiable when both
and are finite and equal
Required condition for function to be differential at x = 1 is
Now, Left-hand limit of the function at x = 1 is
Right-hand limit of the function at x = 1 is
Now, it is clear that
R.H.L. at x= 1 L.H.L. at x= 1 and L.H.L. is not finite as well
Therefore, function is not differentiable at x = 1
Similary, for x = 2
Required condition for function to be differential at x = 2 is
Now, Left-hand limit of the function at x = 2 is
Right-hand limit of the function at x = 1 is
Now, it is clear that
R.H.L. at x= 2 L.H.L. at x= 2 and L.H.L. is not finite as well
Therefore, function is not differentiable at x = 2
Class 12 Maths chapter 5 exercise 5.2 solutions is all about using the chain rule to find derivatives of composite functions. There are a total of 10 questions out of which 8 questions are from chain rule in Class 12 Maths ch 5 ex 5.2. There are 3 examples given before this exercise in the NCERT textbook, that you can solve to understand this concept fully. This concept is very easy as well useful for composite functions. You will find the use of this concept not only in this exercise but in physics, chemistry, and in other chapters also.
Also Read| Continuity and Differentiability Class 12th Chapter 5 Notes
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Also see-
Happy learning!!!
A composite function is obtained from other functions where the output of one function is the input of another function.
sin (x/2) is an example of a composite function.
d(sin(x/2)/dx = cos(x/2)/2
d(cos(x/2)/dx = -sin(x/2)/2
Limit of function is defined as the value of functions reaches when the limit reaches.
Some people consider it hard as it is a new concept included in class 11 maths and the level of maths till class 10 is too easy.
As the foundation of your maths is low, you may find it hard to grasp but with more practice, you will grasp the concept easily.
Yes, You can check here for the NCERT Syllabus for Class 12 Maths. NCERT book exercise questions, NCERT exemplar problems and solutions are helpful to practice questions for the CBSE board exam.
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Hello there! Thanks for reaching out to us at Careers360.
Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.
Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!
Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.
If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.
Let me know if you need any other tips for your math prep. Good luck with your studies!
It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.
Possible steps:
Re-evaluate Your Study Strategies:
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I hope this information helps you.
Hi,
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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.
Thank you and wishing you all the best for your bright future.
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