The standard way of generalizing the derivative is to require it to be linear and to satisfy a version of the product rule. See, for instance, derivations: htt

The standard way of generalizing the derivative is to require it to be linear and to satisfy a version of the product rule. See, for instance, derivations: http://en.wikipedia.org/wiki/Derivation_(differential_algebra) http://en.wikipedia.org/wiki/Derivation_(differential_algebr... In the case of this article, the proposed definition is not linear, so it is indeed a bizarre candidate for a derivative.