Answer
$f'(x) = \dfrac{1+\cos x}{2\sqrt{ 9 + x + \sin x}}$
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 + x + \sin x $
$f(u) = \sqrt{u}$
Derivate the function:
$f'(u) = \dfrac{u'}{2\sqrt{u}}$
Now let's find u'
$u' = 1+\cos x$
Then undo the substitution, simplify and get the answer:
$f'(x) = \dfrac{1+\cos x}{2\sqrt{ 9 + x + \sin x}}$
