Differentiating Inverse Trigonometric Functions
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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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
))
.
QUESTION
What is the chain rule application for
y
=
sec
−
1
(
g
(
x
)
)
y = \sec^{-1}(g(x))
y
=
sec
−
1
(
g
(
x
))
?
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ANSWER
g
′
(
x
)
∣
g
(
x
)
∣
(
g
(
x
)
)
2
−
1
\frac{g'(x)}{|g(x)|\sqrt{(g(x))^2-1}}
∣
g
(
x
)
∣
(
g
(
x
)
)
2
−
1
g
′
(
x
)
. General chain rule pattern for inverse secant composition.
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