# Â  Â Exercise 5.7 ( Differentiation)

Find the second order derivatives of the functions given in Exercises 1 to 10.(Class 12 ncert solution math exercise 5.7 differentiation)

Question:1

Solution: Let y =

Then, differentiate with respect to x

Again differentiate w.r. to x

Question 2:

Solution: Let

Diffrentiate with respect to x

Again d.w.r. to x

Question 3:

Solution: Let

Differentiate .w.r.to x

Again differentiate with respect to x

Question 4:

Solution: Let

Differentiate with respect to x

Again differentiate with respect to x

Question 5:

Solution: Let

Differentiate with respect to x

Again differentiate with respect to x

Question 6:

Solution: Let

Differentiate with respect to x

Again differentiate with respect to x

Question 7:

Solution: Let

Again differentiate with respect to x

Question 8:

Solution: Let

Differentiate with respect to x

Again differentiate with respect to x

Question 9:

Solution: Let

Differentiate with respect to x

Again differentiate with respect to x

Question10:

Solution: Let

Differentiate with respect to x

Again differentiate with respect to x

Question 11: If prove that

Solution: Let

Differentiate with respect to x

Again differentiate with respect to x

Question 12: If Find in term of y alone.

Solution: Since,

Differentiate with respect to x

Again differentiate with respect to x

Question 13: If show that

Solution: Since,

Differentiate with respect to x

Multiply by x both side

Again differentiate with respect to x

Agian multiply by x

Hence proved

Question 14: If show that

Solution: Since,

Differentiate with respect to x

Again differentiate with respect x

L.H.S.

Putting the values

Hence proved

Question 15: If , show that

Solution: Given,

Differentiate with respect to x

Again differentiate with respect to x

Hence proved,

Question 16: If , show that

Solution: Given,

Differentiate with respect to x

Again differentiate with respect to x

L.H.S.

R.H.S.

Hence,

Proved

Question 17: If show that

Solution: Given,

Differentiate with respect to x

Multiply by both side

Again differentiate with respect to x

Again multiply by both side

Hence proved.

## Ncert Solution Chapter 5 : Differention

Ncert Solution solution exercise 5.1

Ncert Solution solution exercise 5.2

Ncert Solution solution exercise 5.3

Ncert Solution solution exercise 5.4

Ncert Solution solution exercise 5.5

Ncert Solution solution exercise 5.6

Ncert Solution solution exercise 5.7

Ncert Solution solution Miscellaneous exercise