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Mathematics
Problem
Given
r
(
u
)
=
⟨
u
2
,
e
u
⟩
r(u)=\langle u^{2},\,e^{u}\rangle
r
(
u
)
=
⟨
u
2
,
e
u
⟩
and
u
=
3
t
−
1
u=3t-1
u
=
3
t
−
1
, determine
d
r
d
t
\dfrac{dr}{dt}
d
t
d
r
. a)
⟨
6
t
−
2
,
e
3
t
−
1
⟩
\langle6t-2,\,e^{3t-1}\rangle
⟨
6
t
−
2
,
e
3
t
−
1
⟩
b)
⟨
6
t
−
2
,
3
e
3
t
−
1
⟩
\langle6t-2,\,3e^{3t-1}\rangle
⟨
6
t
−
2
,
3
e
3
t
−
1
⟩
c)
⟨
18
t
−
6
,
3
e
3
t
−
1
⟩
\langle18t-6,\,3e^{3t-1}\rangle
⟨
18
t
−
6
,
3
e
3
t
−
1
⟩
d)
⟨
2
t
−
2
3
,
1
3
e
3
t
−
1
⟩
\langle2t-\dfrac{2}{3},\,\dfrac{1}{3}e^{3t-1}\rangle
⟨
2
t
−
3
2
,
3
1
e
3
t
−
1
⟩
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