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