Answer
$$ G'(s)= \frac{1}{s^2\sqrt{1-(s^{-1})^2}}.$$
Work Step by Step
Since $ G(s)=\cos^{-1}(s^{-1})$, then the derivative, using the chain rule, is given by
$$ G'(s)=-\frac{1}{\sqrt{1-(s^{-1})^2}}(s^{-1})'=-\frac{-s^{-2}}{\sqrt{1-(s^{-1})^2}}=\frac{1}{s^2\sqrt{1-(s^{-1})^2}}.$$
