Answer
$f'(\theta) = -4 \cos^3\theta\sin\theta$
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
$u = \cos \theta $
$f(u) = u^4$
Derivate the function:
$f'(u) = 4u^3u'$
Now let's find u'
$u' = -\sin \theta$
Then undo the substitution, simplify and get the answer:
$f'(\theta) = -4 \cos^3\theta\sin\theta$
