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Mathematics
Problem
For the parametric equations
x
=
e
t
+
t
x=e^{t}+t
x
=
e
t
+
t
and
y
=
ln
(
2
t
)
y=\ln(2t)
y
=
ln
(
2
t
)
, determine the value of
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
at
t
=
1
t=1
t
=
1
. a)
−
2
e
−
1
(
e
+
1
)
3
-\dfrac{2e-1}{(e+1)^{3}}
−
(
e
+
1
)
3
2
e
−
1
b)
2
e
+
1
(
e
+
1
)
3
\dfrac{2e+1}{(e+1)^{3}}
(
e
+
1
)
3
2
e
+
1
c)
−
2
e
+
1
(
e
+
1
)
3
-\dfrac{2e+1}{(e+1)^{3}}
−
(
e
+
1
)
3
2
e
+
1
d)
−
2
e
+
1
(
e
+
1
)
2
-\dfrac{2e+1}{(e+1)^{2}}
−
(
e
+
1
)
2
2
e
+
1
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