If y = sin (sin x), prove that :

Given,

y = sin (sin x) ……equation 1

To prove:

We notice a second-order derivative in the expression to be proved so first take the step to find the second order derivative.

Let’s find

As

So, lets first find dy/dx

Using chain rule, we will differentiate the above expression

Let t = sin x ⟹

…….equation 2

Again differentiating with respect to x applying product rule:

Using chain rule again in the next step-

[using equation 1 : y =sin (sin x)]

And using equation 2, we have: