- #1

MathematicalPhysicist

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Show that [itex]f_{xy}=0 \forall (x,y)\in \mathbb{R}^2 \Leftrightarrow f(x,y)=g(x)+h(y)[/itex]

The <= is self explanatory, the => I am not sure I got the right reasoning.

I mean we know that from the above we have: [itex]f_x=F(x)[/itex] (it's a question before this one), but now besides taking an integral I don't see how to show the consequent.

Any thoughts how to show this without invoking integration?