Total differential

From Glossary of Meteorology



total differential

The total differential of a function f = f(x1, x2, · · ·, xn) of n variables is defined by the equation
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whether or not x1, x2, · · ·, and xn are independent of each other.
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,
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, · · ·, and
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denote the partial derivatives of f with respect to x1, x2, · · ·, and xn respectively. The total differential df represents the change in f associated with simultaneous infinitesimal changes in x1, x2, · · ·, and xn given by dx1, dx2, · · ·, dxn, respectively, to the order of dx1, dx2, · · ·, dxn.