Question

Differentiate the given function w.r.t. $x$:
$\cos (a\cos x+b\sin x),$ for some constant $a$ and $b$.

Answer 1

Let $y=\cos (a\cos x+b\sin x)$
By using chain rule, we obtain
$\frac{dy}{dx}=\frac{d}{dx}\cos (a\cos x+b\sin x)$
$\Rightarrow \frac{dy}{dx}=-\sin (a\cos x+b\sin x).\frac{d}{dx}(a\cos x+b\sin x)$
$=-\sin (a\cos x+b\sin x).\left[a\right(-\sin )+b\cos x]$
$=(a\sin x-b\cos x).\sin (a\cos x+b\sin x)$