2016 April 07

originally posted on facebook

A quick exercise in L’Hopital’s rule: compute the derivative of

$W((x^2 + x - 1) e^(x - 1))$

at $x = 0$ , where $W$ is the Lambert W function. The derivative of $W$ is given by:

$\frac {dW}{dz} = \frac {W(z)} {z (1 + W(z))}$

(If you wish to be technical about differentiating a function at its branch point, you can consider only $x > 0$ and say that you are taking the limit of the derivative as $x$ goes to zero. Or you can just ignore this note.)

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