## Calculus with Applications (10th Edition)

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