---
tag: 06EH97V2A7
kind: concept
name: Fréchet derivative
aliases: [frechet-derivative, strong-derivative]
msc: [46G05]
uses: [0FNKFT8H6E]
sources:
  - url: https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative
    locator: lead section
same_as:
  wikidata: Q1305350
  wikipedia: Fréchet derivative
---

## Summary

The Fréchet derivative of a map $f$ between normed vector spaces at a point $x$ is a bounded linear map. It best approximates $f(x + h) - f(x)$ for small $h$.
It extends the derivative of one-variable calculus to maps between normed spaces, which can have infinite dimension.
For maps between Euclidean spaces it is the [[total derivative|0FNKFT8H6E]].