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Mathematics
Problem
Let
f
(
x
)
=
x
arccos
x
+
1
−
x
2
f(x)=x\arccos x+\sqrt{1-x^{2}}
f
(
x
)
=
x
arccos
x
+
1
−
x
2
for
−
1
<
x
<
1
-1<x<1
−
1
<
x
<
1
. Evaluate
f
′
(
1
2
)
f'\!\left(\tfrac12\right)
f
′
(
2
1
)
exactly and simplify your answer.
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