Answer
$y' = \frac{{3 - 2\sqrt s }}{{{s^2}}}$
Work Step by Step
$$\eqalign{
& y = \frac{{s - \sqrt s }}{{{s^2}}} \cr
& {\text{Distribute the numerator and simplify}} \cr
& y = \frac{s}{{{s^2}}} - \frac{{\sqrt s }}{{{s^2}}} \cr
& y = \frac{1}{s} - \frac{1}{{{s^{3/2}}}} \cr
& {\text{Rewrite using the property }}\frac{1}{{{x^n}}} = {x^{ - n}} \cr
& y = {s^{ - 1}} - {s^{ - 3/2}} \cr
& {\text{Differentiating}} \cr
& y' = \frac{d}{{ds}}\left[ {{s^{ - 1}}} \right] - \frac{d}{{ds}}\left[ {{s^{ - 3/2}}} \right] \cr
& {\text{Use the differentiation formula }}\frac{d}{{ds}}\left[ {{s^n}} \right] = n{s^{n - 1}} \cr
& y' = - {s^{ - 2}} - \left( { - \frac{3}{2}} \right){s^{ - 5/2}} \cr
& y' = - {s^{ - 2}} + \frac{3}{2}{s^{ - 5/2}} \cr
& y' = - \frac{1}{{{s^2}}} + \frac{3}{{2{s^{5/2}}}} \cr
& {\text{Simplify}} \cr
& y' = \frac{{ - 2{s^{1/2}} + 3}}{{{s^2}}} \cr
& y' = \frac{{3 - 2\sqrt s }}{{{s^2}}} \cr} $$
