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Fréchet Derivative

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

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

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

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

Every function which is Fréchet differentiable is also Carathéodory differentiable.

See also Carathéodory Derivative, Derivative




© 1996-9 Eric W. Weisstein
1999-05-26