Answer
$f'(\theta) = -\dfrac{\csc (\sqrt{\theta-1})}{2\sqrt{\theta-1}}$
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
$u = \sqrt{\theta-1}$
$f(u) = \cot u$
Derivate the function:
$f'(u) = -u'\csc u$
Now let's find u'
$u' = \dfrac{1}{2\sqrt{\theta-1}}$
Then undo the substitution, simplify and get the answer:
$f'(\theta) = -(\dfrac{1}{2\sqrt{\theta-1}})\csc (\sqrt{\theta-1})$
$f'(\theta) = -\dfrac{\csc (\sqrt{\theta-1})}{2\sqrt{\theta-1}}$
