Generalizations of The Derivative - Other Generalizations

Other Generalizations

It may be possible to combine two or more of the above different notions of extension or abstraction of the original derivative. For example, in Finsler geometry, one studies spaces which look locally like Banach spaces. Thus one might want a derivative with some of the features of a functional derivative and the covariant derivative.

The study of stochastic processes requires a form of calculus known as the Malliavin calculus. One notion of derivative in this setting is the H-derivative of a function on an abstract Wiener space.