# Total derivative

From Glossary of Meteorology

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## 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 where and are the partial derivatives of

*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*f*(*x*,*y*) with respect to*x*and*y*, respectively; and 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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