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In mathematics, a total derivative may mean either (i) a differential operator involving the sum of all the partial derivatives with respect to all variables in a problem, or be used compatibly (ii) to express the exterior derivative d, as applied to differential forms, and in particular as applied to a function F considered as a 0-form, so that
- dF(x1, x2, ..., xn) = Σ Fidxi,
where Fi is the partial derivative with respect to xi.
A total differential equation is a differential equation expressed in terms of total derivatives. Since the exterior derivative is a natural operator , in a sense that can be given a technical meaning, such equations are intrinsic and geometric.
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