# Exercise 5.2(Continuity and differentiability)

Differentiate the functions with respect to x in Exercises 1 to 8.(Class 12 ncert solution math exercise 5.2)

Question 1:-

Solution:

Differentiate w.r.t. x

Question 2:-

Solution:-

Differentiate w.r.t. x

Question 3:-

Solution:-

Differentiate w.r.t. x

Question 4:-

Solution:-

Differentiate with respect to x

Question 5:-

Solution:

Differentiate with respect to x

Question 6:-

Solution:

Differentiate with respect to x

Question 7:-

Solution:

Differentiate with respect to x

Question 8:-

Solution:

Differentiate with respect to x

Question 9: Prove that the function given by is not differentiable at .

Solution: Given,

It is known that a function is differentiable at a point in

its domain if both
and are finite and equal.

To check the differentiability of the given function at ,

=-1

=1

Since LHD and RHD at x=1 are not equal,

Therefore, f is not differentiable at .

Question 10: Prove that the greatest integer function defined by is not differentiable at and

Solution:  Given,

It is known that a function is differentiable at a point in its domain if both and are finite and equal.
At ,

Consider the LHD at

Consider RHD at

=0

Since at

Hence, is not differentiable at .

To check the differentiability of the given function at ,
Consider LHD at

Now, consider RHD at

=0

Since, at

Hence, is not differentiable at .