Find d/dt [r(t) · u(t)] and d/dt [r(t) × u(t)] in two different ways.
r(t) = ti + 2t2j + t3k, u(t) = t4k

(a) d/dt [r(t) · u(t)]
(i) Find the product first, then differentiate.
(ii) Apply the properties of the derivative.

(b) d/dt [r(t) × u(t)]
(i) Find the product first, then differentiate.
(ii) Apply the properties of the derivative.

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