Answer
$f'(x) = \dfrac{-5\sin(5x)}{2\sqrt{\cos(5x)}}$
Work Step by Step
First, lets make an «u» substitution in order to make it easier.
$f(u) = \sqrt{u}$
$u = \cos(5x)$
Then lets derivate using the chain rule
$f'(u) = \dfrac{1}{2\sqrt{u}} \times u'$
Now let's find u'
$u' = -5\sin(5x)$
Now let's undo the substitution and simplify
$f'(x) = \dfrac{1}{2\sqrt{\cos(5x)}} \times -5\sin(5x)$
And you got the answer:
$f'(x) = \dfrac{-5\sin(5x)}{2\sqrt{\cos(5x)}}$
