Question

Differentiate the following functions with respect to x.

cos (sin x).

Answer 1

Let y = cos (sin x)

Differentiate both sides w.r.t x, we get

$\frac{dy}{dx}=\frac{d}{dx}\left(cos\right(sinx\left)\right)=-sin\left(sinx\right)\frac{d}{dx}\left(sinx\right)$(By chain rule)

= - sin (sin x) cos x = -cos x sin (sin x)