Question

Compute the derivative

G(s) =
`cos^(-1) (s^(-1))`

I've gotten up to
`1 / ( \sqrt{1-(1/ s^(2) )`
the actual answer says there should be an
`s^(2)` outside of the radical and I'm not sure how to get that.

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-(1)/(s^2)}}\cdot\cfrac{-1}{s^2}\implies \boxed{\cfrac{dg}{ds}=\cfrac{1}{s^2\sqrt{1-(1)/(s^2)}}}`