Gateaux derivative

Summary

The Gateaux derivative of a map between vector spaces at a point measures the rate of change of the map along each direction. It generalizes the directional derivative of calculus to normed and locally convex spaces of any dimension. It is weaker than the Fréchet derivative: a map can have a Gateaux derivative at a point without being continuous there. It is the derivative used in the calculus of variations, where it gives the first variation of a functional.