Second Derivative of Inverse Function

Theorem
Let $f$ be a real function which is of differentiability class $2$.

Let $f$ have an inverse $f^{-1}$, likewise of differentiability class $2$.

Then:
 * $\dfrac {\d^2 x} {\d y^2} = -\dfrac {\d^2 y} {\d x^2} \paren {\dfrac {\d y} {\d x} }^{-3}$