# , for some constant a and b.

Question:

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

Solution:

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

By using chain rule, we obtain

$\frac{d y}{d x}=\frac{d}{d x} \cos (a \cos x+b \sin x)$

$\Rightarrow \frac{d y}{d x}=-\sin (a \cos x+b \sin x) \cdot \frac{d}{d x}(a \cos x+b \sin x)$

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

$=(a \sin x-b \cos x) \cdot \sin (a \cos x+b \sin x)$