Applying Properties of Definite Integrals
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Evaluate
d
d
x
(
1
cot
(
x
)
)
\frac{d}{dx}\bigg(\frac{1}{\text{cot}(x)}\bigg)
d
x
d
(
cot
(
x
)
1
)
.
QUESTION
What is the value of
d
d
x
(
1
x
)
\frac{d}{dx}\bigg(\frac{1}{x}\bigg)
d
x
d
(
x
1
)
?
QUESTION
Evaluate
d
d
x
(
1
csc
(
x
)
)
\frac{d}{dx}\bigg(\frac{1}{\text{csc}(x)}\bigg)
d
x
d
(
csc
(
x
)
1
)
.
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ANSWER
cot
(
x
)
csc
(
x
)
\text{cot}(x)\text{csc}(x)
cot
(
x
)
csc
(
x
)
. Chain rule on
sin
(
x
)
=
(
csc
(
x
)
)
−
1
\sin(x) = (\csc(x))^{-1}
sin
(
x
)
=
(
csc
(
x
)
)
−
1
gives
cos
(
x
)
\cos(x)
cos
(
x
)
.
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