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This is motivated by a question in the Physics SE, but it's a math question not a physical one. For every function $G(x, t)$, can the function be written as a total derivative (wrt $t$) of some other function $F(x, t)$?

A simple counterexample would be fine; hopefully that would be simpler for a poor physicist to understand! A general proof/disproof would be great too.

If it would be easier to take a concrete example, if $G(x, t)$ is $x^2$ can this be written as a total derivative wrt $t$ of some function $F(x, t)$?

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    This is another ambiguous "any". The sentence in the subject line could reasonably be construed as "Is there any function that can be written as a total derivative?". But further context suggests it means "Is it the case that any function, no matter which one, can be written as a total derivative?". Merely changing "any" to "every" would disambiguate it.2012-03-12
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    Many thanks to everyone who answered. I think I have not stated the question precisely enough. I need to take your answers and go away and work out exactly what it it that I'm asking (typical physicist I suppose :-). Thanks again for the help.2012-03-13

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