The Product Rule
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Identify the derivative of
f
(
x
)
=
e
x
×
sin
(
x
)
f(x) = e^x \times \text{sin}(x)
f
(
x
)
=
e
x
×
sin
(
x
)
using the Product Rule.
QUESTION
What is the derivative of
f
(
x
)
=
x
2
×
ln
(
x
)
f(x) = x^2 \times \text{ln}(x)
f
(
x
)
=
x
2
×
ln
(
x
)
using the Product Rule?
QUESTION
Determine the derivative of
f
(
x
)
=
x
2
×
e
x
f(x) = x^2 \times \text{e}^x
f
(
x
)
=
x
2
×
e
x
using the Product Rule.
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ANSWER
2
x
×
e
x
+
x
2
×
e
x
2x \times e^x + x^2 \times e^x
2
x
×
e
x
+
x
2
×
e
x
. Factor out
x
e
x
x e^x
x
e
x
to get
x
e
x
(
2
+
x
)
x e^x(2 + x)
x
e
x
(
2
+
x
)
.
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