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: