Answer
$f'(x)=\dfrac{-4x-18}{x^2+9x}$
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
$u = x^2+9x$
$f(u) = u^{-2}$
Derivate the function:
$f'(u) = -2u^{-1}u'$
Now let's find u'
$u' = 2x+9$
Then undo the substitution, simplify and get the answer:
$f'(x) = -\dfrac{2(2x+9)}{x^2+9x}=\dfrac{-4x-18}{x^2+9x}$
