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Mathematics
Mathematics
Problem
For
x
>
0
x>0
x
>
0
, let
g
(
x
)
=
ln
x
e
3
x
g(x)=\dfrac{\ln x}{e^{3x}}
g
(
x
)
=
e
3
x
ln
x
. Which of the following equals
g
′
(
x
)
g'(x)
g
′
(
x
)
? a)
1
x
+
3
ln
x
e
3
x
\displaystyle \frac{\frac{1}{x}+3\ln x}{e^{3x}}
e
3
x
x
1
+
3
ln
x
b)
1
x
−
ln
x
e
3
x
\displaystyle \frac{\frac{1}{x}-\ln x}{e^{3x}}
e
3
x
x
1
−
ln
x
c)
1
x
−
3
ln
x
e
3
x
\displaystyle \frac{\frac{1}{x}-3\ln x}{e^{3x}}
e
3
x
x
1
−
3
ln
x
d)
1
x
−
3
ln
x
e
6
x
\displaystyle \frac{\frac{1}{x}-3\ln x}{e^{6x}}
e
6
x
x
1
−
3
ln
x
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