# NCERT solution class 12 chapter 5 Continuity and Differentiability exercise 5.5 mathematics part 1

## EXERCISE 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.