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Mathematics
Mathematics
Problem
The parametric equations of a curve are
x
=
e
3
t
,
y
=
e
t
,
t
∈
R
.
x = e^{3t},\qquad y = e^{t},\qquad t\in\mathbb R.
x
=
e
3
t
,
y
=
e
t
,
t
∈
R
.
(i) Evaluate
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
at
t
=
0
t = 0
t
=
0
. (ii) Evaluate
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
at
t
=
0
t = 0
t
=
0
.
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