Answer
$\frac{-3}{2\sqrt[4] {x^5}}$
Work Step by Step
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
$$\frac{dy}{dx} = 6\cdot \frac{-1}{4}x^{-1/4 -1} = \frac{-6}{4}x^{-5/4}$$
$$= \frac{-3}{2}x^{-5/4} =\frac{-3}{2\sqrt[4] {x^5}}$$
