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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
sin
−
1
(
2
x
+
2
4
x
2
+
8
x
+
13
)
f(x) = \sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)
f
(
x
)
=
sin
−
1
(
4
x
2
+
8
x
+
13
2
x
+
2
)
, then the value of
d
(
tan
f
(
x
)
)
d
(
tan
−
1
x
)
\frac{d(\tan f(x))}{d(\tan^{-1} x)}
d
(
t
a
n
−
1
x
)
d
(
t
a
n
f
(
x
))
, when
x
=
1
2
x = \frac{1}{2}
x
=
2
1
, is .....
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