Answer
$y' = -\dfrac{e^x\sin (e^x)}{\cos (e^x)}$
Work Step by Step
In order to derivate this function you have to apply the chain rule
Let's make an «u» substitution to make it easier
$f(u) = \ln(u)$
$u = \cos(e^x)$
Derivate the function:
$f'(u) = \dfrac{u'}{u}$
Now let's find u'
$u'= e^x\sin (e^x)$
Then undo the substitution, simplify and get the answer:
$f'(x) = -\dfrac{e^x\sin (e^x)}{\cos (e^x)}$