Question

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

Answer 1

The correct answer is $=(a\,sin\,x-b\,cos\,x).sin(a\,cosx+b\,sinx)$
Let $y=cos(a\,cosx+b\,sinx)$
By using chain rule, we obtain
$\frac{dy}{dx}=\frac{d}{dx}cos(a\,cosx+b\,sinx)$
$⇒\frac{dy}{dx}=-sin(a\,cosx+b\,sinx).\frac{d}{dx}(a\,cosx+b\,sinx)$
$=-sin(a\,cosx+b\,sinx).[a(-sinx)+b\,cosx]$
$=(a\,sin\,x-b\,cos\,x).sin(a\,cosx+b\,sinx)$