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Mathematics
Problem
A polar curve satisfies
d
y
d
x
=
θ
2
\dfrac{dy}{dx}=\theta^{2}
d
x
d
y
=
θ
2
and
d
x
d
θ
=
θ
\dfrac{dx}{d\theta}=\theta
d
θ
d
x
=
θ
for
θ
>
0
\theta>0
θ
>
0
. What is
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
at
θ
=
2
\theta=2
θ
=
2
? a)
8
8
8
b)
4
4
4
c)
2
2
2
d)
12
12
12
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