- #1
bhatiaharsh
- 9
- 0
Hi,
I remember having read in basic calculus that the following is true, but I don't 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.
I remember having read in basic calculus that the following is true, but I don't 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.