Derivative of inverse error function

Theorem

The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \mathrm{erf}^{-1}(x)=\dfrac{\sqrt{\pi}}{2}e^{[\mathrm{erf}^{-1}(x)]^2},$$ where $\mathrm{erf}^{-1}$ denotes the inverse error function and $\mathrm{erf}$ denotes the error function.