 
Summary: Math 213001
Assignment # 2  Sample answers
1. Compute the requested derivative, first by carrying out the vector op
eration and differentiating the resulting vector or scalar, and then using
differentiation rules.
(a) r(t) = ti  3t3k, u(t) = i + sin(t)k; (d/dt)[r(t) · u(t)];
(b) r(t) = et
i + 2t, f(t) = 4t3
; (d/dt)[f(t)r(t)].
Answer.
(a) r(t) · u(t) = t  3t3
sin(t); then
(r · u) (t) = 1  (9t2
sin(t) + 3t3
cos(t)).
r (t) = i  9t2k and u (t) = cos(t)k. Using the rules,
d
dt
(r(t) · u(t)) = r (t) · u(t) + r(t) · u (t)
= (i  9t2k) · (i + sin(t)k)
