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by
Ciro Santilli
(
@cirosantilli,
34
)
Total derivative
Home
Mathematics
Area of mathematics
Calculus
Derivative
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Updated
2024-12-15
+
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
e
r
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)
Ancestors
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Derivative
Calculus
Area of mathematics
Mathematics
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Total derivative
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1970-01-01
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