Inverse Function Theorem Could anyone please allude to what this one step proof is for this question: !enter image description here

Since the function $\,f^{-1}\,$ is derivable with _no-where zero_ derivative, by the theorem about the derivative of the inverse we get

$$f'=\left[\left(f^{-1}\right)^{-1}\right]'=\frac{1}{\left(f^{-1}\right)'}\ldots$$