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Mathematics
Mathematics
Problem
For a differentiable function
u
(
x
)
≠
0
u(x)\neq 0
u
(
x
)
=
0
, which of the following expressions equals
d
d
x
[
ln
∣
u
(
x
)
∣
]
\dfrac{d}{dx}\bigl[\ln|u(x)|\bigr]
d
x
d
[
ln
∣
u
(
x
)
∣
]
? a)
u
′
(
x
)
ln
∣
u
(
x
)
∣
u'(x)\,\ln|u(x)|
u
′
(
x
)
ln
∣
u
(
x
)
∣
b)
1
u
(
x
)
\dfrac{1}{u(x)}
u
(
x
)
1
c)
u
′
(
x
)
u
(
x
)
\dfrac{u'(x)}{u(x)}
u
(
x
)
u
′
(
x
)
d)
ln
∣
u
′
(
x
)
∣
\ln|u'(x)|
ln
∣
u
′
(
x
)
∣
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