Answer
$f'(\theta) = (1 - \sin \theta)\sec ^2 (\theta + \cos \theta)$
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 = \theta + \cos \theta $
$f(u) = \tan u$
Derivate the function:
$f'(u) = \sec ^2 u$
Now let's find u'
$u' = 1 - \sin \theta$
Then undo the substitution, simplify and get the answer:
$f'(\theta) = (1 - \sin \theta)\sec ^2 (\theta + \cos \theta)$
