Answer
$a)$ $\frac{dV}{dh}=\frac{1}{3}\pi r^{2} $
$b)$ $\frac{dV}{dr}=\frac{2}{3}\pi r h$
Work Step by Step
$a)$
$$\frac{dV}{dh}=\frac{d}{dh}\left(\frac{1}{3}\pi r^{2} h\right)=\frac{1}{3}\pi r^{2}\frac{dh}{dh}=\frac{1}{3}\pi r^{2} $$
$b)$
$$\frac{dV}{dr}=\frac{d}{dr}\left(\frac{1}{3}\pi r^{2} h\right)=\frac{1}{3}\pi h\frac{d}{dr}\left( r^{2} \right)= \frac{1}{3}\pi h2r=\frac{2}{3}\pi r h$$
