The Quotient Rule
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Use the Quotient Rule to differentiate
y
=
6
x
3
x
2
+
2
y = \frac{6x}{3x^2 + 2}
y
=
3
x
2
+
2
6
x
.
QUESTION
Differentiate
f
(
x
)
=
x
2
+
2
x
5
x
+
1
f(x) = \frac{x^2 + 2x}{5x + 1}
f
(
x
)
=
5
x
+
1
x
2
+
2
x
using the Quotient Rule.
QUESTION
Evaluate the derivative:
y
=
4
x
3
x
2
−
2
x
y = \frac{4x^3}{x^2 - 2x}
y
=
x
2
−
2
x
4
x
3
using the Quotient Rule.
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ANSWER
(
x
2
−
2
x
)
(
12
x
2
)
−
4
x
3
(
2
x
−
2
)
(
x
2
−
2
x
)
2
\frac{(x^2 - 2x)(12x^2) - 4x^3(2x - 2)}{(x^2 - 2x)^2}
(
x
2
−
2
x
)
2
(
x
2
−
2
x
)
(
12
x
2
)
−
4
x
3
(
2
x
−
2
)
. Apply quotient rule with
u
=
4
x
3
u = 4x^3
u
=
4
x
3
and
v
=
x
2
−
2
x
v = x^2 - 2x
v
=
x
2
−
2
x
.
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