Differentiating Inverse Trigonometric Functions
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find
d
d
x
(
tan
−
1
(
3
x
)
)
\frac{d}{dx}(\tan^{-1}(\sqrt{3x}))
d
x
d
(
tan
−
1
(
3
x
))
.
QUESTION
Find
d
d
x
(
cos
−
1
(
4
x
3
)
)
\frac{d}{dx}(\cos^{-1}(4x^3))
d
x
d
(
cos
−
1
(
4
x
3
))
.
QUESTION
Find
d
d
x
(
sin
−
1
(
2
x
)
)
\frac{d}{dx}(\sin^{-1}(2x))
d
x
d
(
sin
−
1
(
2
x
))
.
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ANSWER
2
1
−
(
2
x
)
2
\frac{2}{\sqrt{1-(2x)^2}}
1
−
(
2
x
)
2
2
. Chain rule with
d
d
x
(
2
x
)
=
2
\frac{d}{dx}(2x) = 2
d
x
d
(
2
x
)
=
2
applied to
sin
−
1
\sin^{-1}
sin
−
1
formula.
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