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Mathematics
Mathematics
Problem
For differentiable functions
u
(
x
)
u(x)
u
(
x
)
and
v
(
x
)
v(x)
v
(
x
)
with
v
(
x
)
≠
0
v(x)\neq 0
v
(
x
)
=
0
, which of the following equals
d
d
x
(
u
(
x
)
v
(
x
)
)
\dfrac{d}{dx}\Big(\dfrac{u(x)}{v(x)}\Big)
d
x
d
(
v
(
x
)
u
(
x
)
)
? a)
u
′
(
x
)
v
(
x
)
−
u
(
x
)
v
′
(
x
)
v
(
x
)
\dfrac{u'(x)v(x)-u(x)v'(x)}{v(x)}
v
(
x
)
u
′
(
x
)
v
(
x
)
−
u
(
x
)
v
′
(
x
)
b)
u
′
(
x
)
v
(
x
)
−
u
(
x
)
v
′
(
x
)
[
v
(
x
)
]
2
\dfrac{u'(x)v(x)-u(x)v'(x)}{[v(x)]^{2}}
[
v
(
x
)
]
2
u
′
(
x
)
v
(
x
)
−
u
(
x
)
v
′
(
x
)
c)
u
′
(
x
)
v
(
x
)
+
u
(
x
)
v
′
(
x
)
[
v
(
x
)
]
2
\dfrac{u'(x)v(x)+u(x)v'(x)}{[v(x)]^{2}}
[
v
(
x
)
]
2
u
′
(
x
)
v
(
x
)
+
u
(
x
)
v
′
(
x
)
d)
u
(
x
)
v
′
(
x
)
−
u
′
(
x
)
v
(
x
)
[
v
(
x
)
]
2
\dfrac{u(x)v'(x)-u'(x)v(x)}{[v(x)]^{2}}
[
v
(
x
)
]
2
u
(
x
)
v
′
(
x
)
−
u
′
(
x
)
v
(
x
)
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