Can anyone explain to me how to do this problem?
y=ln(cos(4x))
Welcome to the Math Help Forum!
The function $\displaystyle y=\ln\cos (4x)$ may be differentiated by applying the Chain Rule twice, knowing that
$\displaystyle \begin{aligned}
\frac{d}{dx}\ln x&=\frac{1}{x}\\
\frac{d}{dx}\cos x&=-\sin x\\
\frac{d}{dx}(kx)&=k.
\end{aligned}$
For reference, the Chain Rule states that
$\displaystyle \frac{d}{dx}f(g(x))=f'(g(x))g'(x).$