cos(a cos x + b sin x), for some constant a and b.

Let y $=$ cos (a cos x + b sin x) ...(i)

Differentiating (i) on both sides w.r.t. x, we get
$\cfrac{{dy}}{{dx}} = -$ sin (a cos x + b sin x) [a ($-$sin x) + b cos x]

$= -$ sin (a cos x + b sin x) [$-$a sin x + b cos x]
$=$ (a sin x$-$ b cos x) sin (a cos x + b sin x)