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.

You applied the chain rule correctly if you meant to write the derivative as a product of three factors, i.e. $$\dfrac{dy}{dx} = 3(-\sin(\cos x))\cdot(-\sin x).$$ You just need to simplify to get $$--3\sin(\cos x)\cdot \sin x = 3\sin(\cos x)\cdot \sin x$$ which can also be written $$3(\sin x)\sin(\cos x)$$
Writing it as you did, without parentheses, makes it look like $3-\sin(\cos x)( - \sin x)$, which looks like you are subtracting the two trigonometric factors from $3$. 
