Answer
$-2(x+7)^{-3} $
Work Step by Step
We have: $f(x)=(x+7)^{-2}$
We differentiate both sides with respect to $x$.
$f^{\prime}(x)=\dfrac{d}{dx} [(x+7)^{-2}] \\=(-2) (x+7)^{-2-1}\dfrac{d}{dx}(x+7)\\=-2(x+7)^{-3} $
Simplify to obtain:
$f^{\prime}(x)=-2(x+7)^{-3} $
