Image Processing Reference
In-Depth Information
with respect to x
2
R
n
is an n
n matrix, which is
The second derivative of f
(
x
)
de
ned by
2
4
3
5
2
2
f
(
x
)
q
x
1
q
f
(
x
)
q
x
1
q
x
2
f
(
x
)
q
x
1
q
x
n
q
q
2
f
(
x
)
q
x
2
q
x
1
2
f
(
x
)
q
x
2
2
f
(
x
)
q
x
2
q
x
n
q
q
q
2
f
(
x
)
q
x
2
q
¼
(
3
:
207
)
.
.
.
.
2
2
2
f
(
x
)
q
x
n
q
x
1
q
f
(
x
)
q
x
n
q
x
2
q
q
f
(
x
)
q
x
n
Example 3.51
4. Find
q
f
(
x
)
q
x
Let x 2 R
3
and f (x)
¼ x
1
þ
3x
1
þ
2x
2
7x
2
x
3
þ
.
S
OLUTION
2
4
3
5
q
f (x)
q
x
1
q
f (x)
q
x
2
q
f (x)
q
x
3
2
4
3
5
3x
1
þ
6x
1
q
f (x)
q
x
¼
¼
2
7x
3
7x
2
The second derivative is
2
4
3
5
6x
1
þ
600
2
f (x)
q
x
2
q
¼
0
0
7
0
70
Example 3.52
Let x 2 R
n
and f (x)
¼ c
T
x, where c is an n
1 column vector, then
¼ c
T
x ¼ c
1
x
1
þ c
2
x
2
þþc
n
x
n
f (x)
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