Answer
$f'(\theta) = -36\sin(12\theta)(\cos(12\theta))^2$
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
$u = \cos(12\theta)$
$f(u) = u^3$
Derivate the function:
$f'(u) = 3u^2u'$
Now let's find u'
$u' = -12\sin(12\theta)$
Then undo the substitution, simplify and get the answer:
$f'(\theta) = 3(\cos(12\theta))^2(-12\sin(12\theta))$
$f'(\theta) = -36\sin(12\theta)(\cos(12\theta))^2$
