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Mathematics
Mathematics
Problem
The motion of a point on a curve is described parametrically for
t
>
0
t>0
t
>
0
by
x
=
e
3
t
,
y
=
t
2
ln
(
e
t
)
.
x=e^{3t},\qquad y=t^{2}\,\ln(e^{t}).
x
=
e
3
t
,
y
=
t
2
ln
(
e
t
)
.
(i) Obtain
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
in terms of
t
t
t
. (ii) Hence find
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
in terms of
t
t
t
.
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