Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Which of the following gives the correct derivative of
f
(
x
)
g
(
x
)
\dfrac{f(x)}{g(x)}
g
(
x
)
f
(
x
)
with respect to
x
x
x
for
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)
g
′
(
x
)
f
(
x
)
−
f
′
(
x
)
g
(
x
)
[
g
(
x
)
]
2
\dfrac{g'(x)f(x)-f'(x)g(x)}{[g(x)]^{2}}
[
g
(
x
)
]
2
g
′
(
x
)
f
(
x
)
−
f
′
(
x
)
g
(
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
)
[
f
(
x
)
]
2
\dfrac{f'(x)g(x)-f(x)g'(x)}{[f(x)]^{2}}
[
f
(
x
)
]
2
f
′
(
x
)
g
(
x
)
−
f
(
x
)
g
′
(
x
)
Browse the problem library