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Mathematics
Mathematics
Problem
If
u
(
x
)
u(x)
u
(
x
)
and
v
(
x
)
v(x)
v
(
x
)
are differentiable functions, which of the following equals
d
d
x
[
u
(
x
)
v
(
x
)
]
\dfrac{d}{dx}[u(x)v(x)]
d
x
d
[
u
(
x
)
v
(
x
)]
? a)
u
′
(
x
)
v
(
x
)
−
u
(
x
)
v
′
(
x
)
u'(x)v(x)-u(x)v'(x)
u
′
(
x
)
v
(
x
)
−
u
(
x
)
v
′
(
x
)
b)
u
′
(
x
)
v
′
(
x
)
u'(x)v'(x)
u
′
(
x
)
v
′
(
x
)
c)
u
′
(
x
)
v
(
x
)
+
u
(
x
)
v
′
(
x
)
u'(x)v(x)+u(x)v'(x)
u
′
(
x
)
v
(
x
)
+
u
(
x
)
v
′
(
x
)
d)
u
(
x
)
v
′
(
x
)
u(x)v'(x)
u
(
x
)
v
′
(
x
)
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