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I don't understand where or how many times I need to apply the chain rule.

daOnlyBG
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Carly
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  • The form of this function is a bit tricky. I would convert/rewrite it to a form $f(x) = e^{g(x)}$ so that it would have a more familiar look. – hardmath Oct 29 '14 at 03:00

1 Answers1

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Hint:

Let $\cos x^{ \ln (3x) } = y $. Then

$$ \ln(3x) \ln( \cos x) = \ln y $$

Now, apply implicit differentiation:

$$ \frac{1}{x} \ln( \cos x ) + \ln(3x) \frac{ - \sin x }{\cos x } = \frac{y'}{y}$$

Now, solve for $y'$