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