Answer
$f'(\theta) = 4\theta \csc (9 - 2\theta ^2) \cot (9 - 2\theta ^2)$
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
$u = 9 - 2\theta ^2$
$f(u) = \csc u$
Derivate the function:
$f'(u) = -u' \csc u \cot u$
Now let's find u'
$u' = -4\theta$
Then undo the substitution, simplify and get the answer:
$f'(\theta) = -(-4\theta) \csc (9 - 2\theta ^2) \cot (9 - 2\theta ^2)$
$f'(\theta) = 4\theta \csc (9 - 2\theta ^2) \cot (9 - 2\theta ^2)$
