Answer
$\displaystyle \frac{ds}{dt}=(-3r^{-4}+0.5r^{-0.5})\cdot\frac{dr}{dt}$
Work Step by Step
$r=r(t)$ so, by the chain rule,
$\displaystyle \frac{ds}{dt}=\frac{ds}{dr}\frac{dr}{dt}$
$\displaystyle \frac{ds}{dr}=\frac{d}{dr}[r^{-3}+r^{0.5}]=-3r^{-4}+0.5r^{-0.5}$
$\displaystyle \frac{ds}{dt}=(-3r^{-4}+0.5r^{-0.5})\cdot\frac{dr}{dt}$