Rates of Change
AP Precalculus · Flashcards
AP PRECALCULUS · FLASHCARDS
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QUESTION
What is the derivative of
f
(
x
)
=
arccsc
(
x
)
f(x) = \text{arccsc}(x)
f
(
x
)
=
arccsc
(
x
)
?
QUESTION
Identify the derivative of
f
(
x
)
=
e
x
f(x) = e^x
f
(
x
)
=
e
x
.
QUESTION
What is the derivative of
f
(
x
)
=
log
a
(
x
)
f(x) = \log_a(x)
f
(
x
)
=
lo
g
a
(
x
)
?
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ANSWER
f
′
(
x
)
=
1
x
ln
(
a
)
f'(x) = \frac{1}{x \ln(a)}
f
′
(
x
)
=
x
l
n
(
a
)
1
. Change of base gives factor
1
ln
(
a
)
\frac{1}{\ln(a)}
l
n
(
a
)
1
.
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