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

#### Question 1:

Differentiate the function with respect to x.

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.

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.

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.

xx
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
v = 2sin 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.

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.

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.

= (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.

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.

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.

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.

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.

The given function is
Let xy = u and yx = 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.

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.

The given function is
Taking logarithm on both the sides, we obtain
Differentiating both sides, we obtain

#### Question 15:

Find of function.

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.

The given relationship is
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain

#### Question 18:

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