Third Derivative of Inverse Function

Theorem
Let $f$ be a real function which is of differentiability class $3$.

Let $f$ have an inverse $f^{-1}$, likewise of differentiability class $3$.

Then:
 * $\dfrac {\d^3 x} {\d y^3} = -\paren {\dfrac {\d^3 y} {\d x^3} \dfrac {\d y} {\d x} - 3 \paren {\dfrac {\d^2 y} {\d x^2} }^2} \paren {\dfrac {\d y} {\d x} }^{-5}$