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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