## NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability Ex 5.5

#### Page No 178:

#### Question 1:

Differentiate the function with respect to

*x*.#### Answer:

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain#### Question 2:

Differentiate the function with respect to

*x*.#### Answer:

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain#### Question 3:

Differentiate the function with respect to

*x*.#### Answer:

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain#### Question 4:

Differentiate the function with respect to

*x*.#### Answer:

*u*=

*x*

^{x}

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain*v*= 2

^{sin }

^{x}

Taking logarithm on both the sides with respect to

*x*, we obtain
Differentiating both sides with respect to

*x*, we obtain#### Question 5:

Differentiate the function with respect to

*x*.#### Answer:

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain#### Question 6:

Differentiate the function with respect to

*x*.#### Answer:

Differentiating both sides with respect to

*x*, we obtain
Differentiating both sides with respect to

*x*, we obtain
Therefore, from (1), (2), and (3), we obtain

#### Question 7:

Differentiate the function with respect to

*x*.#### Answer:

*u*= (log

*x*)

^{x}

Differentiating both sides with respect to

*x*, we obtain
Differentiating both sides with respect to

*x*, we obtain
Therefore, from (1), (2), and (3), we obtain

#### Question 8:

Differentiate the function with respect to

*x*.#### Answer:

Differentiating both sides with respect to

*x*, we obtain
Therefore, from (1), (2), and (3), we obtain

#### Question 9:

Differentiate the function with respect to

*x*.#### Answer:

Differentiating both sides with respect to

*x*, we obtain
Differentiating both sides with respect to

*x*, we obtain
From (1), (2), and (3), we obtain

#### Question 10:

Differentiate the function with respect to

*x*.#### Answer:

Differentiating both sides with respect to

*x*, we obtain
Differentiating both sides with respect to

*x*, we obtain
From (1), (2), and (3), we obtain

#### Question 11:

Differentiate the function with respect to

*x*.#### Answer:

Differentiating both sides with respect to

*x*, we obtain
Differentiating both sides with respect to

*x*, we obtain
From (1), (2), and (3), we obtain

#### Question 12:

Find of function.

#### Answer:

The given function is

Let

*x*^{y}=*u*and*y*^{x}=*v*
Then, the function becomes

*u*+*v*= 1
Differentiating both sides with respect to

*x*, we obtain
Differentiating both sides with respect to

*x*, we obtain
From (1), (2), and (3), we obtain

#### Question 13:

Find of function.

#### Answer:

The given function is

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain#### Question 14:

Find of function.

#### Answer:

The given function is

Taking logarithm on both the sides, we obtain

Differentiating both sides, we obtain

#### Question 15:

Find of function.

#### Answer:

The given function is

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain#### Question 16:

Find the derivative of the function given by and hence find.

#### Answer:

The given relationship is

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to

*x*, we obtain#### Page No 179:

#### Question 18:

If

*u*,*v*and*w*are functions of*x*, then show that
in two ways-first by repeated application of product rule, second by logarithmic differentiation.

#### Answer:

Let

By applying product rule, we obtain

By taking logarithm on both sides of the equation, we obtain

Differentiating both sides with respect to

*x*, we obtain_{}

^{}