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Mathematics
Mathematics
Problem
Which of the following gives the derivative of
f
(
x
)
g
(
x
)
\dfrac{f(x)}{g(x)}
g
(
x
)
f
(
x
)
where
f
f
f
and
g
g
g
are differentiable and
g
(
x
)
≠
0
g(x)\neq 0
g
(
x
)
=
0
? a)
f
′
(
x
)
g
(
x
)
+
f
(
x
)
g
′
(
x
)
[
g
(
x
)
]
2
\dfrac{f'(x)g(x)+f(x)g'(x)}{[g(x)]^{2}}
[
g
(
x
)
]
2
f
′
(
x
)
g
(
x
)
+
f
(
x
)
g
′
(
x
)
b)
f
′
(
x
)
g
′
(
x
)
\dfrac{f'(x)}{g'(x)}
g
′
(
x
)
f
′
(
x
)
c)
f
′
(
x
)
g
(
x
)
−
f
(
x
)
g
′
(
x
)
[
g
(
x
)
]
2
\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^{2}}
[
g
(
x
)
]
2
f
′
(
x
)
g
(
x
)
−
f
(
x
)
g
′
(
x
)
d)
f
′
(
x
)
g
(
x
)
−
f
(
x
)
g
′
(
x
)
g
(
x
)
\dfrac{f'(x)g(x)-f(x)g'(x)}{g(x)}
g
(
x
)
f
′
(
x
)
g
(
x
)
−
f
(
x
)
g
′
(
x
)
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