Evaluate
WOLFRAM

DEMONSTRATIONS
PROJECT
Derivatives of Quintic Polynomials
coefficient
of
x
5
x
4
x
3
x
2
x
constant
term
interval

10
≤
x
≤
10
x
reset
F
(
x
)
=

3
x
5
+
2
x
4
+
3
x
3
+
5
x
2
+
3
x
+
4
The
first
derivative
is
:
F
′
(
x
)
=

15
x
4
+
8
x
3
+
9
x
2
+
10
x
+
3
For
x
equal
to
2
,
F
′
(
2
)
=

117
The
second
derivative
is
:
F
′
′
(
x
)
=

60
x
3
+
24
x
2
+
18
x
+
10
For
x
equal
to
2
,
F
′
′
(
2
)
=

338
The
third
derivative
is
:
F
(
3
)
(
x
)
=

180
x
2
+
48
x
+
18
For
x
equal
to
2
,
F
(
3
)
(
2
)
=

606
The
fourth
derivative
is
:
F
(
4
)
(
x
)
=
48

360
x
For
x
equal
to
2
,
F
(
4
)
(
2
)
=

672
This Demonstration calculates the first four derivatives of
F
(
x
)
=
c
5
x
5
+
c
4
x
4
+
c
3
x
3
+
c
2
x
2
+
c
1
x
+
c
0
and evaluates them at
x
for

10
≤
x
≤
10
.