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Question
Mathematics
If f (x)=(5x/(1-x)2/3)+cos2(2x+1), then f'(0) =
Q. If
f
(
x
)
=
(
1
−
x
)
2/3
5
x
+
co
s
2
(
2
x
+
1
)
, then
f
′
(
0
)
=
3609
208
Continuity and Differentiability
Report Error
A
5
+
2
s
in
2
9%
B
5
+
2
cos
2
12%
C
5
−
2
s
in
2
71%
D
5
−
2
cos
2
7%
Solution:
f
(
x
)
=
5
x
(
1
−
x
)
−
3
2
+
co
s
2
(
2
x
+
1
)
f
′
(
x
)
=
5
{
x
×
3
−
2
(
1
−
x
)
−
5/3
(
−
1
)
+
(
1
−
x
)
−
2/3
×
1
}
+
2
cos
(
2
x
+
1
)
{
−
s
in
(
2
x
+
1
)
×
2
}
⇒
f
′
(
x
)
=
5
(
1
−
x
)
−
3
2
+
3
10
x
(
1
−
x
)
−
3
5
−
2
s
in
(
4
x
+
2
)
∴
f
′
(
0
)
=
5
−
2
s
in
2
.