Answer
$$\frac{{dy}}{{ds}} = \frac{{{5^{\sqrt s }}\ln 5}}{{2\sqrt s }}$$
Work Step by Step
$$\eqalign{
& y = {5^{\sqrt s }} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}s \cr
& \frac{{dy}}{{ds}} = \frac{d}{{ds}}\left[ {{5^{\sqrt s }}} \right] \cr
& {\text{use the rule }}\frac{d}{{dx}}\left[ {{a^u}} \right] = {a^x}\ln a\frac{{du}}{{dx}}. \cr
& {\text{For this exercise}}{\text{, let }}a = 5.{\text{ and }}u = \sqrt s,{\text{ }}x = s.{\text{ Then}}{\text{,}} \cr
& \frac{{dy}}{{ds}} = {5^{\sqrt s }}\ln 5\frac{d}{{ds}}\left[ {\sqrt s } \right] \cr
& {\text{solve the derivative and simplify}} \cr
& \frac{{dy}}{{ds}} = {5^{\sqrt s }}\ln 5\left( {\frac{1}{{2\sqrt s }}} \right) \cr
& \frac{{dy}}{{ds}} = \frac{{{5^{\sqrt s }}\ln 5}}{{2\sqrt s }} \cr} $$
