[tex]\bf g(s)=cos^{-1}(s^{-1})\\\\
-----------------------------\\\\
\cfrac{dg}{ds}=\cfrac{-1}{\sqrt{1-s^{-2}}}\cdot -s^{-2}\implies \cfrac{dg}{ds}=\cfrac{-1}{\sqrt{1-s^{-2}}}\cdot\cfrac{-1}{s^2}\impliedby
\begin{array}{llll}
using\ the\\
chain-rule
\end{array}
\\\\\\
\cfrac{dg}{ds}=\cfrac{-1}{\sqrt{1-\frac{1}{s^2}}}\cdot\cfrac{-1}{s^2}\implies \boxed{\cfrac{dg}{ds}=\cfrac{1}{s^2\sqrt{1-\frac{1}{s^2}}}}[/tex]
