NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability Ex 5.7

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