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Mathematics
Mathematics
Problem
If
f
(
x
)
=
x
cos
x
x
2
+
1
+
sin
x
f(x)=\dfrac{x\cos x}{x^{2}+1}+\sin x
f
(
x
)
=
x
2
+
1
x
cos
x
+
sin
x
, find
f
′
(
π
2
)
f'\!\left(\dfrac{\pi}{2}\right)
f
′
(
2
π
)
. a)
−
π
π
2
+
4
-\dfrac{\pi}{\pi^{2}+4}
−
π
2
+
4
π
b)
2
π
π
2
+
4
\dfrac{2\pi}{\pi^{2}+4}
π
2
+
4
2
π
c)
−
2
π
π
2
+
4
-\dfrac{2\pi}{\pi^{2}+4}
−
π
2
+
4
2
π
d)
−
2
π
π
2
+
2
-\dfrac{2\pi}{\pi^{2}+2}
−
π
2
+
2
2
π
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