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Mathematics
Mathematics
Problem
Let
A
(
x
)
=
∫
1
x
3
ln
t
t
d
t
A(x)=\displaystyle\int_{1}^{x^{3}}\frac{\ln t}{t}\,dt
A
(
x
)
=
∫
1
x
3
t
ln
t
d
t
for
x
>
0
x>0
x
>
0
. Which of the following equals
A
′
(
x
)
A'(x)
A
′
(
x
)
? a)
ln
x
x
\displaystyle\frac{\ln x}{x}
x
ln
x
b)
ln
(
x
3
)
3
x
2
\displaystyle\frac{\ln(x^{3})}{3x^{2}}
3
x
2
ln
(
x
3
)
c)
3
ln
(
x
3
)
x
\displaystyle\frac{3\,\ln(x^{3})}{x}
x
3
ln
(
x
3
)
d)
3
x
2
ln
x
\displaystyle3x^{2}\ln x
3
x
2
ln
x
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