Lambert W function Calculator

Let $w(x)$ be a real-valued function satisfying the equation \[w(x)\mathrm{e}^{w(x)}=x\] this application finds $w(x)$ and its derivative $w'(x)$. For example, given $x=2$ we get $w(2)=0.8526$ and $w'(2)=0.2301$

Note that this calculator is for real numbers only, excluding complex numbers, so $x$ must be greater than or equal to $-\frac{1}{\mathrm{e}}$. We have two solutions of the equation above when $-\frac{1}{\mathrm{e}} < x < 0$ and one for $x\geqslant 0$.

Input Data

Enter $x$ as a real number or math expression of real numbers.

Lambert W function Calculator