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Carathéodory Derivative


A function f is Carathéodory differentiable at a if there exists a function phi which is continuous at a such that

 f(x)-f(a)=phi(x)(x-a).

Every function which is Carathéodory differentiable is also Fréchet differentiable.


See also

Derivative, Fréchet Derivative

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Cite this as:

Weisstein, Eric W. "Carathéodory Derivative." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CaratheodoryDerivative.html

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