Derivative of Exponential Integral Function

Theorem
Let $\Ei: \R_{>0} \to \R$ denote the exponential integral function:


 * $\map \Ei x = \ds \int_{t \mathop = x}^{t \mathop \to +\infty} \frac {e^{-t} } t \rd t$

Then:
 * $\dfrac \d {\d x} \paren {\map \Ei x} = -\dfrac {e^{-x} } x$