## Calculus with Applications (10th Edition)

$\frac{-3}{2\sqrt[4] {x^5}}$
Let's rewrite $$y = \frac{6}{\sqrt[4] x}$$ as: $$y = 6x^{-1/4}.$$ We can then use the Power Rule, which says that $\frac{d}{dx}(x^n) = nx^{n-1}$, to find that $$\frac{dy}{dx} = 6\cdot \frac{-1}{4}x^{-1/4 -1} = \frac{-6}{4}x^{-5/4}$$ $$= \frac{-3}{2}x^{-5/4} =\frac{-3}{2\sqrt[4] {x^5}}$$