## NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability Ex 5.2

#### Question 1:

Differentiate the functions with respect to x.

Let f(x)=sinx2+5, ux=x2+5, and v(t)=sint

Then, vou=vux=vx2+5=tanx2+5=f(x)
Thus, f is a composite of two functions.
Alternate method

#### Question 2:

Differentiate the functions with respect to x.

Thus, is a composite function of two functions.
Put t = u (x) = sin x
By chain rule,
Alternate method

#### Question 3:

Differentiate the functions with respect to x.

Thus, is a composite function of two functions, u and v.
Put t = u (x) = ax + b
Hence, by chain rule, we obtain
Alternate method

#### Question 4:

Differentiate the functions with respect to x.

Thus, is a composite function of three functions, u, v, and w.
Hence, by chain rule, we obtain
Alternate method

#### Question 5:

Differentiate the functions with respect to x.

The given function is, where g (x) = sin (ax + b) and
h (x) = cos (cx d)
∴ is a composite function of two functions, u and v.
Therefore, by chain rule, we obtain
h is a composite function of two functions, p and q.
Put y = p (x) = cx d
Therefore, by chain rule, we obtain

#### Question 6:

Differentiate the functions with respect to x.

The given function is.

#### Question 7:

Differentiate the functions with respect to x.

#### Question 8:

Differentiate the functions with respect to x.

Clearly, is a composite function of two functions, and v, such that
By using chain rule, we obtain
Alternate method

#### Question 9:

Prove that the function given by
is notdifferentiable at x = 1.

The given function is
It is known that a function f is differentiable at a point x = c in its domain if both
are finite and equal.
To check the differentiability of the given function at x = 1,
consider the left hand limit of f at x = 1
Since the left and right hand limits of f at x = 1 are not equal, f is not differentiable at x = 1

#### Question 10:

Prove that the greatest integer function defined byis not
differentiable at x = 1 and x = 2.