## EXERCISE 5.4

#### Page No 174:

#### Question 1:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the quotient rule, we obtain

#### Question 2:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the chain rule, we obtain

#### Question 3:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the chain rule, we obtain

#### Question 4:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the chain rule, we obtain

#### Question 5:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the chain rule, we obtain

#### Question 6:

Differentiate the following w.r.t. *x*:

#### Answer:

#### Question 7:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

Then,

By differentiating this relationship with respect to *x*, we obtain

#### Question 8:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the chain rule, we obtain

, *x* > 1

#### Question 9:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the quotient rule, we obtain

#### Question 10:

Differentiate the following w.r.t. *x*:

#### Answer:

Let

By using the chain rule, we obtain