Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Function in terms of its partial derivatives

Loading...

Similar Threads - Function terms partial | Date |
---|---|

I Vector Calculus: What do these terms mean? | Dec 2, 2016 |

Why is an integrated function with multiple terms... | Jan 4, 2016 |

Expressing an integral in terms of gamma functions | Dec 23, 2015 |

Calculation boundary terms of a functional | Sep 24, 2013 |

Write a complex valued function in terms of z | May 25, 2013 |

**Physics Forums - The Fusion of Science and Community**