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Mathematics
Mathematics
Problem
The curve is defined by
x
=
e
t
x=e^{t}
x
=
e
t
and
y
=
t
2
e
t
y=t^{2}e^{t}
y
=
t
2
e
t
for all real
t
t
t
. Express
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
entirely in terms of
x
x
x
. a)
2
(
1
+
ln
x
)
x
\displaystyle 2\bigl(1+\ln x\bigr)x
2
(
1
+
ln
x
)
x
b)
2
(
1
+
ln
x
)
x
\displaystyle \frac{2\bigl(1+\ln x\bigr)}{x}
x
2
(
1
+
ln
x
)
c)
2
+
2
ln
x
x
2
\displaystyle \frac{2+2\ln x}{x^{2}}
x
2
2
+
2
ln
x
d)
2
(
1
+
ln
x
)
\displaystyle 2\bigl(1+\ln x\bigr)
2
(
1
+
ln
x
)
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