# Total Differential

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Related to Total Differential: Total differential equation

## total differential

[′tōd·əl ‚dif·ə′ren·chəl] (mathematics)

The total differential of a function of several variables, ƒ(

*x*_{1},*x*_{2},…,*x*_{n }), is the function given by the sum of terms (∂ƒ/∂*x*_{i })*dx*_{i }as*i*runs from 1 to*n*. Also known as differential.## Total Differential

The total differential of a function *f(x, y*, z, …) of several independent variables is

Define the increment of f as

*∆ f = f(x +∆ x, y + ∆ y, z + ∆z,…*)

- *f*(*x, y, z*,…)

then as

tends to zero, so does the difference Δf — *df.*