The Product Rule
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the derivative of
y
=
(
x
+
3
)
(
x
2
−
x
+
1
)
y = (x + 3)(x^2 - x + 1)
y
=
(
x
+
3
)
(
x
2
−
x
+
1
)
.
QUESTION
What is the derivative of
f
(
x
)
=
x
2
×
sin
(
x
)
f(x) = x^2 \times \text{sin}(x)
f
(
x
)
=
x
2
×
sin
(
x
)
?
QUESTION
Find
d
/
d
x
d/dx
d
/
d
x
of
f
(
x
)
=
x
2
×
sec
(
x
)
f(x) = x^2 \times \text{sec}(x)
f
(
x
)
=
x
2
×
sec
(
x
)
. Use Product Rule.
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ANSWER
2
x
×
sec
(
x
)
+
x
2
×
sec
(
x
)
tan
(
x
)
2x \times \text{sec}(x) + x^2 \times \text{sec}(x)\text{tan}(x)
2
x
×
sec
(
x
)
+
x
2
×
sec
(
x
)
tan
(
x
)
. Product Rule:
(
x
2
)
′
×
sec
(
x
)
+
x
2
×
(
sec
(
x
)
)
′
(x^2)' \times \sec(x) + x^2 \times (\sec(x))'
(
x
2
)
′
×
sec
(
x
)
+
x
2
×
(
sec
(
x
)
)
′
.
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