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Mathematics
Problem
For an invertible differentiable function
f
f
f
, let
a
a
a
be a real number such that
f
(
a
)
=
b
f(a)=b
f
(
a
)
=
b
. Which of the following expressions is equal to
(
f
−
1
)
′
(
b
)
(f^{-1})'(b)
(
f
−
1
)
′
(
b
)
? a)
1
f
′
(
a
)
\dfrac{1}{f'(a)}
f
′
(
a
)
1
b)
f
′
(
a
)
f'(a)
f
′
(
a
)
c)
1
f
′
(
b
)
\dfrac{1}{f'(b)}
f
′
(
b
)
1
d)
−
1
f
′
(
a
)
-\dfrac{1}{f'(a)}
−
f
′
(
a
)
1
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