Question

Differenciate cos(sin x)

Answer 1

the above answer is right answer for your question

Answer 2

There are two functions here in the question.
1) cos function
and the
2) sin function.

Let f(y) = cos ( sin x )

Let u = sin x

Therefore,
f(y) = cos u

By applying the chain rule for differentiation,

dy/dx = dy/du + du/dx
dy/dx = d ( cos u ) / du + d sin x / d x
= - sin u + cos x
= - sin ( sin x) + cos x
since, u = sin x

= cos x - sin ( sin x )

Therefore,
d [ cos ( sin x )] / dx = cos x - sin ( sin x)

Hope this helps you !!