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Mathematics
Mathematics
Problem
If
u
(
t
)
=
⟨
sin
t
,
cos
t
,
t
⟩
\mathbf{u}(t) = \langle \sin t, \cos t, t \rangle
u
(
t
)
=
⟨
sin
t
,
cos
t
,
t
⟩
and
v
(
t
)
=
⟨
t
,
cos
t
,
sin
t
⟩
\mathbf{v}(t) = \langle t, \cos t, \sin t \rangle
v
(
t
)
=
⟨
t
,
cos
t
,
sin
t
⟩
, use Formula 4 of Theorem 3 to find
d
d
t
[
u
(
t
)
⋅
v
(
t
)
]
\frac{d}{dt} [\mathbf{u}(t) \cdot \mathbf{v}(t)]
d
t
d
[
u
(
t
)
⋅
v
(
t
)]
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