Derivative of erfi

Theorem

The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{erfi}(z) = \dfrac{2}{\sqrt{\pi}} e^{z^2},$$ where $\mathrm{erfi}$ denotes the imaginary error function, $\pi$ denotes pi, and $e^{z^2}$ denotes the exponential function.