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Mathematics
Mathematics
Problem
If
f
(
x
)
=
sin
−
1
(
2
x
1
+
x
2
)
f(x) = \sin^{-1} \left( \frac{2x}{1+x^2} \right)
f
(
x
)
=
sin
−
1
(
1
+
x
2
2
x
)
, then a. Statement I The value of
f
′
(
2
)
=
−
2
5
f'(2) = -\frac{2}{5}
f
′
(
2
)
=
−
5
2
. b. Statement II
f
(
x
)
=
sin
−
1
(
2
x
1
+
x
2
)
=
−
2
1
+
x
2
f(x) = \sin^{-1} \left( \frac{2x}{1+x^2} \right) = \frac{-2}{1+x^2}
f
(
x
)
=
sin
−
1
(
1
+
x
2
2
x
)
=
1
+
x
2
−
2
, for
x
>
1
x > 1
x
>
1
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