Total derivative

From Glossary of Meteorology



total derivative

The rate of change of a function of two or more variables with reference to a parameter on which these variables are dependent.

If z = f(x, y, t), x = φ(t), and y = θ(t), the total derivative of z with reference to t, written dz/dt, is given by
ams2001glos-Te37
where
ams2001glos-Tex04
and
ams2001glos-Tex05
are the partial derivatives of f(x, y) with respect to x and y, respectively;
ams2001glos-Tex06
and
ams2001glos-Tex07
are the total derivatives of φ(t) and θ(t), respectively, with respect to t. For a function of one variable, the partial derivative equals the total derivative. The individual derivative is the total derivative when the parameter t represents time.


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