Can anyone explain to me how to do this problem?

y=ln(cos(4x))

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- Nov 7th 2009, 03:45 PMiheartphysics01Differentiating functions with natural logs
Can anyone explain to me how to do this problem?

y=ln(cos(4x)) - Nov 7th 2009, 03:53 PMScott H
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

$\displaystyle \frac{d}{dx}f(g(x))=f'(g(x))g'(x).$ - Nov 7th 2009, 03:53 PMVonNemo19
- Nov 7th 2009, 04:06 PMiheartphysics01
ok thanks so much!(Happy)

i will probably be using this forum a lot!