what is the derivative of $3\cos(\cos x)\;?$ what is the derivative of $3\cos(\cos x)\;?$
I think I need to use the chain rule and i believed it to be $3-\sin(\cos x)(-\sin x)$ but this is not the case.

Take a deep breath and start with the derivative of the inner part:
$$
\cos'(x) = -\sin x
$$
then you use $$
(3\cos)' u = -3u'\sin u
$$with $u=\cos x$:
$$
\frac d{dx} 3\cos(\cos x) = -3(-\sin x) \sin(\cos x)
= 3\sin x \sin(\cos x)
$$
