# Total Differential of the First Order

Total Differential of the First Order

The total differential of a function of two variables is given by definition: . Then its total increment is given by , where and as . The differential is the principal part of , which means that more rapidly than as .

dz=dx+dy

f

x

f

y

Δz=dz+η

η=ϵρ

ϵ0

ρ=

d+d

02

x

2

y

dz

Δz

η=ϵρ0

dz0

ρ0