If $n$ is a positive integer, one can show that $\frac{d}{dx}(\sin^n{x}\cos{nx})=n\sin^{n-1}{x}\cos(n+1)x$ (by the appropriate differentiation rules and the trigonometric identity for $\cos(\alpha + \beta)$ ).
Find a similar formula for the derivative of $y=\cos^n{x}\cos{nx}$.

$y' =$