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I remember having read in basic calculus that the following is true, but I dont know what this property is called and am having a hard time finding a reference to this.

[tex]d u(x,y) = \frac{\partial u}{\partial x} dx + \frac{\partial u}{\partial y} dy[/tex]

Ques: Is this true ? Is this true for all functions? Or is there a condition that the function u should be separable ?

I also think that if this is true, then I should be able to reconstruct the function u by taking the anti-derivative of the above equation:

[tex]\int d u(x,y) = \int \frac{\partial u}{\partial x} dx + \int \frac{\partial u}{\partial y} dy[/tex]

However, this fails when

[tex]u(x,y) = x^2y^2[/tex]

Am I missing something here ? If the above holds only for separable functions, is there a way I can reconstruct a function from its partial derivatives ?

Any guidance is appreciated. Thanks.

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# Function in terms of its partial derivatives

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