A differential of the form d f = P(x, y) d x + Q(x, y) d y is exact (also called a total differential) if integral d f is path-independent. This will be true if d f = (df)/(dx) d x + (df)/(dy) d y, so P and Q must be of the form P(x, y) = (df)/(dx) Q(x, y) = (df)/(dy).
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