AP Calculus BC Quiz
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DIFFERENTIATION: DEFINITION AND FUNDAMENTAL PROPERTIES
Question 1
of 20
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For
g
(
x
)
=
ln
x
x
3
g(x)=\dfrac{\ln x}{x^3}
g
(
x
)
=
x
3
ln
x
, what is
g
′
(
x
)
g'(x)
g
′
(
x
)
?
A
(
1
x
)
(
x
3
)
−
(
ln
x
)
(
3
x
2
)
(
x
3
)
2
\dfrac{\left(\dfrac{1}{x}\right)(x^3)-(\ln x)(3x^2)}{(x^3)^2}
(
x
3
)
2
(
x
1
)
(
x
3
)
−
(
ln
x
)
(
3
x
2
)
B
(
1
x
)
(
x
3
)
+
(
ln
x
)
(
3
x
2
)
(
x
3
)
2
\dfrac{\left(\dfrac{1}{x}\right)(x^3)+(\ln x)(3x^2)}{(x^3)^2}
(
x
3
)
2
(
x
1
)
(
x
3
)
+
(
ln
x
)
(
3
x
2
)
C
(
ln
x
)
(
3
x
2
)
−
(
1
x
)
(
x
3
)
(
x
3
)
2
\dfrac{(\ln x)(3x^2)-\left(\dfrac{1}{x}\right)(x^3)}{(x^3)^2}
(
x
3
)
2
(
ln
x
)
(
3
x
2
)
−
(
x
1
)
(
x
3
)
D
(
1
x
)
(
x
3
)
−
(
ln
x
)
(
3
x
2
)
x
3
\dfrac{\left(\dfrac{1}{x}\right)(x^3)-(\ln x)(3x^2)}{x^3}
x
3
(
x
1
)
(
x
3
)
−
(
ln
x
)
(
3
x
2
)
E
(
1
x
)
(
x
3
)
−
(
ln
x
)
(
3
x
2
)
x
6
\dfrac{\left(\dfrac{1}{x}\right)(x^3)-(\ln x)(3x^2)}{x^6}
x
6
(
x
1
)
(
x
3
)
−
(
ln
x
)
(
3
x
2
)
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