Total differential

(Math.)

the differential of a function of two or more variables, when each of the variables receives an increment. The total differential of the function is the sum of all the partial differentials.

Total Differential

total differential

[′tōd·əl ‚dif·ə′ren·chəl] (mathematics) The total differential of a function of several variables, ƒ(x₁, x₂,…, x_n), is the function given by the sum of terms (∂ƒ/∂ x_i) dx_ias 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.

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