# NCERT solution class 12 chapter 5 Continuity and Differentiability exercise 5.7 mathematics part 1

## EXERCISE 5.7

#### Question 1:

Find the second order derivatives of the function.

Let

Then,

#### Question 2:

Find the second order derivatives of the function.

Let

Then,

#### Question 3:

Find the second order derivatives of the function.

Let

Then,

#### Question 4:

Find the second order derivatives of the function.

Let

Then,

#### Question 5:

Find the second order derivatives of the function.

Let

Then,

#### Question 6:

Find the second order derivatives of the function.

Let

Then,

#### Question 7:

Find the second order derivatives of the function.

Let

Then,

#### Question 8:

Find the second order derivatives of the function.

Let

Then,

#### Question 9:

Find the second order derivatives of the function.

Let

Then,

#### Question 10:

Find the second order derivatives of the function.

Let

Then,

#### Question 11:

If, prove that

It is given that,

Then,

Hence, proved.

#### Question 12:

If findin terms of y alone.

It is given that,

Then,

#### Question 13:

If, show that

It is given that,

Then,

Hence, proved.

#### Question 14:

Ifshow that

It is given that,

Then,

Hence, proved.

#### Question 15:

If, show that

It is given that,

Then,

Hence, proved.

#### Question 16:

If, show that

The given relationship is

Taking logarithm on both the sides, we obtain

Differentiating this relationship with respect to x, we obtain

Hence, proved.

If, show that