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Product spaces differentiablility

Mathematics Asked by Robert-ben on January 5, 2021

Let $E_1,E_2,F$ three finite dimensional vector spaces. And let $f$ a mapping defined on $E_1times E_2 rightarrow F$ : My question is that if $f$ is differentiable with respect to $x$ (its first variable) and $y$ (second variable), can we deduce that $f$ is differentiable ?

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