Derivative of an Inverse Function

Let $f$ be a function that is differentiable on an interval $I.$ If $f$ possesses an inverse function $g$ , then $g$ is differentiable at any $x$ for which $f'(g(x))\ne 0.$ Moreover,

$$g'(x)=\frac{1}{f'(g(x))}\;,\quad f'(g(x))\ne 0.$$