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Total derivative
Index
Mathematics
Fields of mathematics
Applied mathematics
Mathematical physics
Lagrangian mechanics
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1970-01-01
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Lagrangian mechanics
Mathematical physics
Applied mathematics
Fields of mathematics
Mathematics
Index
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Total derivative
by
Ciro Santilli
37
Updated
2025-06-02
+
Created
1970-01-01
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The
total derivative
of
a
function assigns for every point of the domain
a
linear map
with same domain, which is the best
linear approximation
to the function value around this point,
i
.e. the
tangent
plane.
E.
g
. in 1D:
T
o
t
a
l
d
er
i
v
a
t
i
v
e
=
D
[
f
(
x
0
)]
(
x
)
=
f
(
x
0
)
+
∂
x
∂
f
(
x
0
)
×
x
(1)
and in 2D:
D
[
f
(
x
0
,
y
0
)]
(
x
,
y
)
=
f
(
x
0
,
y
0
)
+
∂
x
∂
f
(
x
0
,
y
0
)
×
x
+
∂
y
∂
f
(
x
0
,
y
0
)
×
y
(2)
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