Answer
$\displaystyle \frac{dy}{dx}=\frac{-30x}{(3x^{2}-4)^{6}}$
Work Step by Step
$y=\displaystyle \frac{1}{(3x^{2}-4)^{5}}=(3x^{2}-4)^{-5}=[w(x)]^{-5}$
Use the chain rule.
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[w(x)]^{-5}$
$\displaystyle \frac{dy}{dx}=-5(w(x))^{-6}\cdot w^{\prime}(x)$
$\displaystyle \frac{dy}{dx}=-5(3x^{2}-4)^{-6}\cdot 6x$
$\displaystyle \frac{dy}{dx}=-30x(3x^{2}-4)^{-6}$
$\displaystyle \frac{dy}{dx}=\frac{-30x}{(3x^{2}-4)^{6}}$
