Answer
$f'(\theta) = 9(-2\sin \theta + 5\cos \theta)(2\cos \theta + 5 \sin \theta)^8$
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 = 2\cos \theta + 5 \sin \theta $
$f(u) = u^9 $
Derivate the function:
$f'(u) = 9u^8u'$
Now let's find u'
$u' = -2\sin \theta + 5\cos \theta$
Then undo the substitution, simplify and get the answer:
$f'(\theta) = 9(-2\sin \theta + 5\cos \theta)(2\cos \theta + 5 \sin \theta)^8$
