# NCERT Solutions for Exercise 5.7 Class 12 Maths Chapter 5 - Continuity and Differentiability

In the previous exercises, you have learned about finding the first-order differentiation of different types of functions. In NCERT solutions for Class 12 Maths chapter 5 exercise 5.7, you will learn about finding the derivatives of second order. If a function y=f(x) is given, you can find its first-order derivative by differentiation of y y w.r.t x i.e. f'(x) = dy/dx and if you again differentiate f'(x) w.r.t the x, you will get the second-order f''(x).

If you have command on the first-order differentiation then exercise 5.7 Class 12 Maths will be very easy for you as you just need to differentiate the given function two times. The first and second-order derivatives are useful in finding minimum and maximum values of the functions, finding the domain and range of the function, other subjects also. If you looking for the NCERT solutions in one place, click on the above link. You will get NCERT solutions from Classes 6 to 12 for Science and Maths.

**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 5.5
- Continuity and Differentiability Exercise 5.6
- Continuity and Differentiability Exercise 5.8
- Continuity and Differentiability Miscellaneous Exercise

**Continuity and Differentiability Exercise: 5.7**

**Question:1 **Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, second order derivative

Therefore, the second order derivative is

**Question:2** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, the second-order derivative is

Therefore, second-order derivative is

**Question:3** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, the second-order derivative is

Therefore, the second-order derivative is

**Question:4** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, second order derivative is

Therefore, second order derivative is

**Question:5** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, the second-order derivative is

Therefore, the second-order derivative is

**Question:6** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, second order derivative is

Therefore, second order derivative is

**Question:7** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, second order derivative is

Therefore, second order derivative is

**Question:8 ** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Now, differentiation w.r.t. x

Now, second order derivative is

Therefore, second order derivative is

**Question:9** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Now, differentiation w.r.t. x

Now, second order derivative is

Therefore, second order derivative is

**Question:10** Find the second order derivatives of the functions given in Exercises 1 to 10.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, second order derivative is

Using Quotient rule

Therefore, second order derivative is

**Question:11 ** If prove that

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, the second-order derivative is

Now,

Hence proved

**Question:12 ** If Find in terms of y alone.

**Answer:**

Given function is

Now, differentiation w.r.t. x

Now, second order derivative is

-(i)

Now, we want in terms of y

Now, put the value of x in (i)

Therefore, answer is

**Question:13 **If , show that

**Answer:**

Given function is

Now, differentiation w.r.t. x

-(i)

Now, second order derivative is

By using the Quotient rule

-(ii)

Now, from equation (i) and (ii) we will get

Now, we need to show

Put the value of from equation (i) and (ii)

Hence proved

**Question:14 ** If , show that

**Answer:**

Given function is

Now, differentiation w.r.t. x

-(i)

Now, second order derivative is

-(ii)

Now, we need to show

Put the value of from equation (i) and (ii)

Hence proved

**Question:15** If , show that **Answer:**

Given function is

Now, differentiation w.r.t. x

-(i)

Now, second order derivative is

-(ii)

Now, we need to show

Put the value of from equation (ii)

Hence, L.H.S. = R.H.S.

Hence proved

**Question:16** If show that

**Answer:**

Given function is

We can rewrite it as

Now, differentiation w.r.t. x

-(i)

Now, second order derivative is

-(ii)

Now, we need to show

Put value of from equation (i) and (ii)

Hence, L.H.S. = R.H.S.

Hence proved

**Question:17** If show that

**Answer:**

Given function is

Now, differentiation w.r.t. x

-(i)

Now, the second-order derivative is

By using the quotient rule

-(ii)

Now, we need to show

Put the value from equation (i) and (ii)

Hence, L.H.S. = R.H.S.

Hence proved

**More About NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7**

In Class 12th Maths chapter 5 exercise 5.7, you will get 17 questions related to finding the second-order derivatives. There are four examples given in the NCERT book prior to the ex 5.7 which you can solve to get more familiar with second derivatives before solving the exercise question. After solving examples, you can try to solve Class 12th Maths chapter 5 exercise 5.7 questions. You may not be to solve these exercise 5.7 Class 12 Maths problems by yourself at first. You can go through Class 12 Maths chapter 5 exercise 5.7 solutions to get conceptual clarity.

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

**Benefits of ****NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7**

**Benefits of**

**NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7**

- Class 12 Maths chapter 5 exercise 5.7 solutions are designed in a descriptive manner that you can understand easily.
- Don't go through NCERT solutions for Class 12 Maths chapter 5 exercise 5.7 without trying to solve NCERT problems by yourself.
- You can use exercise 5.7 Class 12 Maths solutions for reference.

**Also see-**

NCERT Solutions for Class 12 Maths Chapter 5

NCERT Exemplar Solutions Class 12 Maths Chapter 5

**NCERT Solutions of Class 12 Subject Wise**

## NCERT Solutions for Class 12 Maths

NCERT Solutions for Class 12 Physics

NCERT Solutions for Class 12 Chemistry

NCERT Solutions for Class 12 Biology

**Subject Wise NCERT Exampler Solutions**

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!!!**

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