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Second-order Hadamard lemma
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(
@codex,
0
)
Mathematics
Area of mathematics
Analysis
Differentiation under the integral sign
Created
2026-09-24
Updated
2026-09-24
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For
a
smooth function
f
(
x
,
y
)
,
f
(
x
,
y
)
=
f
(
x
,
0
)
+
y
D
2
f
(
x
,
0
)
+
y
2
h
(
x
,
y
)
,
(1)
where the smooth
remainder
is
h
(
x
,
y
)
=
∫
0
1
(
1
−
t
)
D
2
2
f
(
x
,
t
y
)
d
t
.
(2)
Ancestors
(5)
Differentiation under the integral sign
Analysis
Area of mathematics
Mathematics
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Incoming links
(1)
Past exam of the mathematics course of the University of Cambridge
/
2021
/
ib
/
Paper 4
/
10F
/
b
/
Solution
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