## EXERCISE 5.7

#### Page No 183:

#### Question 1:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 2:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 3:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 4:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 5:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 6:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 7:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 8:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 9:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 10:

Find the second order derivatives of the function.

#### Answer:

Let

Then,

#### Question 11:

If, prove that

#### Answer:

It is given that,

Then,

Hence, proved.

#### Page No 184:

#### Question 12:

If findin terms of *y* alone.

#### Answer:

It is given that,

Then,

#### Question 13:

If, show that

#### Answer:

It is given that,

Then,

Hence, proved.

#### Question 14:

Ifshow that

#### Answer:

It is given that,

Then,

Hence, proved.

#### Question 15:

If, show that

#### Answer:

It is given that,

Then,

Hence, proved.

#### Question 16:

If, show that

#### Answer:

The given relationship is

Taking logarithm on both the sides, we obtain

Differentiating this relationship with respect to *x*, we obtain

Hence, proved.

#### Question 17:

If, show that

#### Answer:

The given relationship is

Then,

Hence, proved.