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Mathematics
Problem
Let
g
(
x
)
=
ln
(
1
+
e
4
x
)
g(x)=\ln\!\left(\sqrt{1+e^{4x}}\right)
g
(
x
)
=
ln
(
1
+
e
4
x
)
. Which of the following is equal to
g
′
(
x
)
g'(x)
g
′
(
x
)
? a)
e
4
x
1
+
e
4
x
\dfrac{e^{4x}}{1+e^{4x}}
1
+
e
4
x
e
4
x
b)
2
e
4
x
1
+
e
4
x
\dfrac{2e^{4x}}{1+e^{4x}}
1
+
e
4
x
2
e
4
x
c)
2
1
+
e
4
x
\dfrac{2}{1+e^{4x}}
1
+
e
4
x
2
d)
4
e
4
x
1
+
e
4
x
\dfrac{4e^{4x}}{1+e^{4x}}
1
+
e
4
x
4
e
4
x
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