Answer
$$
D_{x}\left[\frac{8}{\sqrt[4]{x}}-\frac{3}{\sqrt{x^{3}}}\right]=-2 x^{-5 / 4}+\frac{9}{2} x^{-5 / 2}
$$
Work Step by Step
\begin{align*}
D_{x}\left[\frac{8}{\sqrt[4]{x}}-\frac{3}{\sqrt{x^{3}}}\right]&=D_{x}\left[\frac{8}{\sqrt[4]{x}}\right]-D_{x}\left[\frac{3}{\sqrt{x^{3}}}\right]\\
&=\frac{d}{dx}\left[8x^{-1/4}\right]-\frac{d}{dx}\left[3x^{-1/3}\right] ,\ \ \left(\text{Use } \frac{d}{dx} (x^n)=nx^{n-1}\right) \\
&= -2 x^{-5 / 4}+\frac{9}{2} x^{-5 / 2}\\
\end{align*}
