Differentiating Inverse Functions
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Which inverse function has a derivative of
−
1
1
+
x
2
-\frac{1}{1+x^2}
−
1
+
x
2
1
?
QUESTION
Find the derivative of
y
=
arccos
(
5
x
)
y = \text{arccos}(5x)
y
=
arccos
(
5
x
)
at
x
=
0
x = 0
x
=
0
.
QUESTION
Find
(
f
−
1
)
′
(
2
)
(f^{-1})'(2)
(
f
−
1
)
′
(
2
)
if
f
(
x
)
=
e
x
f(x) = e^x
f
(
x
)
=
e
x
and
f
(
a
)
=
2
f(a) = 2
f
(
a
)
=
2
.
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ANSWER
1
2
\frac{1}{2}
2
1
. Since
f
(
ln
2
)
=
2
f(\ln 2) = 2
f
(
ln
2
)
=
2
and
f
′
(
ln
2
)
=
2
f'(\ln 2) = 2
f
′
(
ln
2
)
=
2
, so
(
f
−
1
)
′
(
2
)
=
1
2
(f^{-1})'(2) = \frac{1}{2}
(
f
−
1
)
′
(
2
)
=
2
1
.
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