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Fréchet Derivative

A function $f$ is Fréchet differentiable at $a$ if

\lim_{x\to a} {f(x)-f(a)\over x-a}

exists. This is equivalent to the statement that $\phi$ has a removable Discontinuity at $a$, where

\phi(x)\equiv {f(x)-f(a)\over x-a}.

Every function which is Fréchet differentiable is also Carathéodory differentiable.

See also Carathéodory Derivative, Derivative

© 1996-9 Eric W. Weisstein