WOLFRAM|DEMONSTRATIONS PROJECT

Total Differential of the First Order

​
f(x,y)=
2
x
+
2
y
xy
1-
2
x
-
2
y
x
0.4
y
0.3
dx
0.3
dy
0.3
surface opacity
0.3
thickness
0.1
show axes
show horizontal plane
show tangent plane
show text
show additional text
The total differential of a function of two variables is given by definition:
dz=
f
x
dx+
f
y
dy
. Then its total increment is given by
Δz=dz+η
, where
η=ϵρ
and
ϵ0
as
ρ=
d
2
x
+d
2
y
0
. The differential
dz
is the principal part of
Δz
, which means that
η=ϵρ0
more rapidly than
dz0
as
ρ0
.