##  [Fréchet Derivative](/frechet-derivative) 

  ##  [Fréchet Derivative](https://natural.quantumdictionary.io/frechet-derivative-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The Fréchet derivative of a map f between Banach spaces at a point x is the bounded linear operator Df(x) that best approximates f near x, meaning f(x+h) = f(x) + Df(x)[h] + o(‖h‖) as h→0.