The term is from "exact differential".

While any thing of the form f(x,y,z)dx+ g(x,y,z)dy+ h(x,y,z)dz

**looks** like the differentiall of some F(x,y,z), it may not be. Given any function F(x,y,z), its differential is

. that comes from the chain rule:

for any parameter, t.

In order that f(x,y)dx+ g(x,y)dy+ h(x,y)dz be a "real" (or "exact") differential, we must have and the same for the other mixed derivatives.

Back in Calculus III such a thing was called an "exact differential" (some texts use the term "conservative" in analogy with "conservative force fields" in physics but I dislike using physics terms in mathematics). In the theory of "differential forms" on manifolds, a differential form,

, of order n, is called "exact" if there exist some differential form [itex]\alpha[/itex], of order n-1, such that [itex]\omega= d\alpha[/itex].