#### Answer

$f'(\theta) = -9\sin(9\theta +41)$

#### 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
$u = 9\theta +41$
$f(u) = \cos(u)$
Derivate the function:
$f'(u) = -u'\cos(u)$
Now let's find u'
$u' = 9$
Then undo the substitution, simplify and get the answer:
$f'(\theta) = -9\sin(9\theta +41)$