##  [Gâteaux Differentiability](/gateaux-differentiability) 

  ##  [Gâteaux Differentiability](https://puremath.quantumdictionary.io/gateaux-differentiability-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A weaker, directional notion of differentiability: at a point x the directional derivative along each vector v exists, i.e. the limit lim_{t→0} (f(x+tv)-f(x))/t exists for every v. It records first-order directional rates but does not a priori require a single bounded linear approximant.