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Mathematics
Mathematics
Problem
Which of the following expressions equals the derivative of
g
(
x
)
=
ln
x
e
2
x
g(x)=\ln x\,e^{2x}
g
(
x
)
=
ln
x
e
2
x
for
x
>
0
x>0
x
>
0
? a)
e
2
x
(
1
x
+
ln
x
)
e^{2x}\left(\dfrac{1}{x}+\ln x\right)
e
2
x
(
x
1
+
ln
x
)
b)
e
2
x
(
1
x
+
2
ln
x
)
e^{2x}\left(\dfrac{1}{x}+2\ln x\right)
e
2
x
(
x
1
+
2
ln
x
)
c)
e
2
x
(
1
x
−
2
ln
x
)
e^{2x}\left(\dfrac{1}{x}-2\ln x\right)
e
2
x
(
x
1
−
2
ln
x
)
d)
e
2
x
(
2
+
ln
x
x
)
e^{2x}\left(2+\dfrac{\ln x}{x}\right)
e
2
x
(
2
+
x
ln
x
)
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