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Mathematics
Mathematics
Problem
For differentiable vector-valued functions
r
(
t
)
\mathbf r(t)
r
(
t
)
and
s
(
t
)
\mathbf s(t)
s
(
t
)
, which of the following equals
d
d
t
(
r
(
t
)
⋅
s
(
t
)
)
\displaystyle \frac{d}{dt}\big(\mathbf r(t)\cdot\mathbf s(t)\big)
d
t
d
(
r
(
t
)
⋅
s
(
t
)
)
? a)
r
′
(
t
)
⋅
s
′
(
t
)
\mathbf r'(t)\cdot\mathbf s'(t)
r
′
(
t
)
⋅
s
′
(
t
)
b)
r
′
(
t
)
⋅
s
(
t
)
−
r
(
t
)
⋅
s
′
(
t
)
\mathbf r'(t)\cdot\mathbf s(t)-\mathbf r(t)\cdot\mathbf s'(t)
r
′
(
t
)
⋅
s
(
t
)
−
r
(
t
)
⋅
s
′
(
t
)
c)
r
′
(
t
)
⋅
s
(
t
)
+
r
(
t
)
⋅
s
′
(
t
)
\mathbf r'(t)\cdot\mathbf s(t)+\mathbf r(t)\cdot\mathbf s'(t)
r
′
(
t
)
⋅
s
(
t
)
+
r
(
t
)
⋅
s
′
(
t
)
d)
r
′
(
t
)
⋅
s
(
t
)
\mathbf r'(t)\cdot\mathbf s(t)
r
′
(
t
)
⋅
s
(
t
)
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