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Mathematics
Mathematics
Problem
For
0
<
x
<
1
0<x<1
0
<
x
<
1
, find
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
where
y
=
x
arctan
(
1
−
x
2
)
y = x\,\arctan\bigl(\sqrt{1-x^{2}}\bigr)
y
=
x
arctan
(
1
−
x
2
)
. Express your answer in simplified form.
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