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Mathematics
Mathematics
Problem
For
x
>
0
x>0
x
>
0
, find
d
d
x
[
x
x
(
ln
x
)
4
]
\dfrac{d}{dx}\bigl[x^{x}(\ln x)^{4}\bigr]
d
x
d
[
x
x
(
ln
x
)
4
]
. a)
x
x
(
ln
x
)
4
(
ln
x
+
4
x
ln
x
)
x^{x}(\ln x)^{4}\left(\ln x + \dfrac{4}{x\ln x}\right)
x
x
(
ln
x
)
4
(
ln
x
+
x
ln
x
4
)
b)
x
x
(
ln
x
)
4
(
ln
x
+
1
)
x^{x}(\ln x)^{4}\left(\ln x + 1\right)
x
x
(
ln
x
)
4
(
ln
x
+
1
)
c)
x
x
(
ln
x
)
4
(
1
+
4
x
ln
x
)
x^{x}(\ln x)^{4}\left(1 + \dfrac{4}{x\ln x}\right)
x
x
(
ln
x
)
4
(
1
+
x
ln
x
4
)
d)
x
x
(
ln
x
)
4
(
ln
x
+
1
+
4
x
ln
x
)
x^{x}(\ln x)^{4}\left(\ln x + 1 + \dfrac{4}{x\ln x}\right)
x
x
(
ln
x
)
4
(
ln
x
+
1
+
x
ln
x
4
)
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