Answer
$\displaystyle \frac{ds}{dt}=(1-r^{-2})\cdot\frac{dr}{dt}$
Work Step by Step
$r=r(t)$ so, by the chain rule,
$\displaystyle \frac{ds}{dt}=\frac{ds}{dr}\frac{dr}{dt}$
$\displaystyle \frac{ds}{dr}=\frac{d}{dr}[r+r^{-1}]=1-r^{-2}$
$\displaystyle \frac{ds}{dt}=(1-r^{-2})\cdot\frac{dr}{dt}$