How do I differentiate $\sin(x)^{\cos(x^3)}$? I'm taking a calc 1 class and I have come across a function that I'm having difficulty finding answers on the web.
$y=\sin(x)^{\cos(x^3)}$
I know there's some chain rule to apply, but what do I do with the cos(x)?
I am assuming this:
$y' = \cos(x^3).(\sin(x)')^{\cos(x^3) - 1}$
Is my thinking correct?

Use that
$$y=e^{\cos (x^3)\log(\sin x)}$$
and by chain rule we have
$$y=e^{f(x)}\implies y'=f'(x)e^{f(x)}$$
