Question

Compute the derivative

Answer 1

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