Answer
$-(2s+s^{0.5})^{-2}\cdot(2+0.5s^{-0.5})$
Work Step by Step
$r(s)$ is a composite function.
Let $u(x)=x^{-1},\qquad v(s)=2s+s^{0.5}$
$\displaystyle \frac{du}{dx}=-x^{-2}, \quad\frac{dv}{ds}=2+0.5s^{-0.5}$
Then,$\quad r(s)=u(v(s))$ and $\displaystyle \frac{dr}{ds}=\frac{du}{dv}\frac{dv}{ds}$
$\displaystyle \frac{du}{dv}=-v^{-2}=-(2s+s^{0.5})^{-2}$
$\displaystyle \frac{dr}{ds}=\frac{du}{dv}\frac{dv}{ds}=-(2s+s^{0.5})^{-2}\cdot(2+0.5s^{-0.5})$
