Find the derivative of f(x)=erf(x)f(x) = \text{erf}(x)f(x)=erf(x) where erf(x)=2π∫0xe−t2dt\text{erf}(x) = \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dterf(x)=π2∫0xe−t2dt.
2πe−x2\frac{2}{\sqrt{\pi}} e^{-x^2}π2e−x2
e−x2e^{-x^2}e−x2
1πe−x2\frac{1}{\sqrt{\pi}} e^{-x^2}π1e−x2
−2xe−x2-2x e^{-x^2}−2xe−x2