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Mathematics
Problem
Let
f
(
x
)
=
ln
(
x
2
1
+
e
x
)
f(x)=\ln\left(\dfrac{x^2}{1+e^{x}}\right)
f
(
x
)
=
ln
(
1
+
e
x
x
2
)
. Which of the following is
f
′
(
x
)
f'(x)
f
′
(
x
)
? a)
2
x
+
e
x
1
+
e
x
\dfrac{2}{x}+\dfrac{e^{x}}{1+e^{x}}
x
2
+
1
+
e
x
e
x
b)
2
x
−
e
x
1
+
e
x
\dfrac{2}{x}-\dfrac{e^{x}}{1+e^{x}}
x
2
−
1
+
e
x
e
x
c)
(
2
x
)
(
1
+
e
x
)
−
x
2
e
x
(
1
+
e
x
)
2
\dfrac{(2x)(1+e^{x})-x^{2}e^{x}}{(1+e^{x})^{2}}
(
1
+
e
x
)
2
(
2
x
)
(
1
+
e
x
)
−
x
2
e
x
d)
1
x
−
e
x
1
+
e
x
\dfrac{1}{x}-\dfrac{e^{x}}{1+e^{x}}
x
1
−
1
+
e
x
e
x
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