Differentiation of Functional Powers

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Functional power rule
(f^g)' = \left(e^{g\ln f}\right)' = f^g\left(f'{g \over f} + g'\ln f\right),\qquad f > 0

I can rarely see a use for this in physics (luckily most of our exponentials have a constant, natural base!), however it handles cases I wouldn't otherwise usually know how to deal with. Proof to come.

This page was recovered in October 2009 from the Plasmagicians page on Differentiation_of_Functional_Powers dated 07:58, 6 October 2006.

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