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Mathematics
Mathematics
Problem
The parametric equations
x
(
t
)
=
ln
t
x(t)=\ln t
x
(
t
)
=
ln
t
and
y
(
t
)
=
t
2
+
1
y(t)=t^{2}+1
y
(
t
)
=
t
2
+
1
are valid for
t
>
0
t>0
t
>
0
. Find an explicit formula for
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
in terms of
x
x
x
(eliminate
t
t
t
from your final answer).
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