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Mathematics
Mathematics
Problem
The variables
x
x
x
and
y
y
y
are related by
sin
y
=
3
x
2
\sin y=3x^{2}
sin
y
=
3
x
2
for
−
1
3
<
x
<
1
3
-\dfrac13<x<\dfrac13
−
3
1
<
x
<
3
1
and
y
y
y
in
(
−
π
2
,
π
2
)
\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)
(
−
2
π
,
2
π
)
. Which expression equals
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
in terms of
x
x
x
only? a)
6
x
1
−
9
x
4
6x\sqrt{1-9x^{4}}
6
x
1
−
9
x
4
b)
6
x
1
−
9
x
4
\dfrac{6x}{1-9x^{4}}
1
−
9
x
4
6
x
c)
6
x
1
−
9
x
4
\dfrac{6x}{\sqrt{1-9x^{4}}}
1
−
9
x
4
6
x
d)
6
x
1
−
9
x
2
\dfrac{6x}{\sqrt{1-9x^{2}}}
1
−
9
x
2
6
x
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