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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
log
5
(
3
x
−
2
)
+
4
ln
x
,
x
>
2
3
.
g(x)=\log_5(3x-2)+4\ln x, \quad x>\frac23.
g
(
x
)
=
lo
g
5
(
3
x
−
2
)
+
4
ln
x
,
x
>
3
2
.
(i) Find
g
′
(
x
)
g'(x)
g
′
(
x
)
. (ii) Hence calculate the value of
g
′
(
4
)
g'(4)
g
′
(
4
)
, giving your answer correct to three decimal places.
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