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Mathematics
Problem
Define
v
(
t
)
=
t
2
+
1
v(t)=t^{2}+1
v
(
t
)
=
t
2
+
1
,
u
(
v
)
=
v
3
u(v)=v^{3}
u
(
v
)
=
v
3
, and
r
(
u
)
=
⟨
u
cos
u
,
ln
(
1
+
u
2
)
⟩
\mathbf r(u)=\langle u\cos u,\,\ln(1+u^{2})\rangle
r
(
u
)
=
⟨
u
cos
u
,
ln
(
1
+
u
2
)⟩
. Determine
d
r
d
t
\dfrac{d\mathbf r}{dt}
d
t
d
r
when
t
=
1
t=1
t
=
1
.
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