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Mathematics
Problem
Let
f
f
f
be differentiable and invertible with
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
′
(
1
)
=
2
f'(1)=2
f
′
(
1
)
=
2
. Define
h
(
x
)
=
cos
(
f
−
1
(
x
)
)
h(x)=\cos\bigl(f^{-1}(x)\bigr)
h
(
x
)
=
cos
(
f
−
1
(
x
)
)
. Evaluate
h
′
(
4
)
h'(4)
h
′
(
4
)
.
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