AP Calculus AB Quiz
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DIFFERENTIATION: DEFINITION AND FUNDAMENTAL PROPERTIES
Question 1
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For
q
(
x
)
=
ln
(
x
+
1
)
x
q(x)=\dfrac{\ln(x+1)}{x}
q
(
x
)
=
x
ln
(
x
+
1
)
, what is
q
′
(
x
)
q'(x)
q
′
(
x
)
?
A
1
x
+
1
⋅
x
−
ln
(
x
+
1
)
⋅
1
x
2
\dfrac{\frac{1}{x+1}\cdot x-\ln(x+1)\cdot 1}{x^2}
x
2
x
+
1
1
⋅
x
−
ln
(
x
+
1
)
⋅
1
B
1
x
+
1
⋅
x
+
ln
(
x
+
1
)
⋅
1
x
2
\dfrac{\frac{1}{x+1}\cdot x+\ln(x+1)\cdot 1}{x^2}
x
2
x
+
1
1
⋅
x
+
ln
(
x
+
1
)
⋅
1
C
1
x
+
1
⋅
x
−
ln
(
x
+
1
)
x
\dfrac{\frac{1}{x+1}\cdot x-\ln(x+1)}{x}
x
x
+
1
1
⋅
x
−
ln
(
x
+
1
)
D
1
x
(
x
+
1
)
\dfrac{1}{x(x+1)}
x
(
x
+
1
)
1
E
1
x
+
1
⋅
x
−
ln
(
x
+
1
)
x
2
+
1
\dfrac{\frac{1}{x+1}\cdot x-\ln(x+1)}{x^2+1}
x
2
+
1
x
+
1
1
⋅
x
−
ln
(
x
+
1
)
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