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Mathematics
Mathematics
Problem
Let
h
(
x
)
=
x
2
arcsin
(
2
x
)
h(x)=x^{2}\arcsin(2x)
h
(
x
)
=
x
2
arcsin
(
2
x
)
. Determine
h
′
(
x
)
h'(x)
h
′
(
x
)
. a)
2
x
arcsin
(
2
x
)
+
x
2
1
−
4
x
2
2x\arcsin(2x)+\dfrac{x^{2}}{\sqrt{1-4x^{2}}}
2
x
arcsin
(
2
x
)
+
1
−
4
x
2
x
2
b)
arcsin
(
2
x
)
+
2
x
1
−
4
x
2
\arcsin(2x)+\dfrac{2x}{\sqrt{1-4x^{2}}}
arcsin
(
2
x
)
+
1
−
4
x
2
2
x
c)
2
x
arcsin
(
2
x
)
+
2
x
2
1
−
4
x
2
2x\arcsin(2x)+\dfrac{2x^{2}}{\sqrt{1-4x^{2}}}
2
x
arcsin
(
2
x
)
+
1
−
4
x
2
2
x
2
d)
2
x
arcsin
(
2
x
)
+
2
x
2
1
+
4
x
2
2x\arcsin(2x)+\dfrac{2x^{2}}{\sqrt{1+4x^{2}}}
2
x
arcsin
(
2
x
)
+
1
+
4
x
2
2
x
2
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