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Mathematics
Mathematics
Problem
Given
r
(
t
)
=
⟨
t
,
t
2
,
1
⟩
r(t)=\langle t, t^{2}, 1\rangle
r
(
t
)
=
⟨
t
,
t
2
,
1
⟩
and
s
(
t
)
=
⟨
cos
t
,
sin
t
,
t
⟩
s(t)=\langle \cos t, \sin t, t\rangle
s
(
t
)
=
⟨
cos
t
,
sin
t
,
t
⟩
, determine
d
d
t
(
r
(
t
)
⋅
s
(
t
)
)
\displaystyle \frac{d}{dt}\big(r(t)\cdot s(t)\big)
d
t
d
(
r
(
t
)
⋅
s
(
t
)
)
at
t
=
π
t=\pi
t
=
π
.
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