Chapter 12.2, Problem 37E

Using Two MethodsIn Exercises 37 and 38, find (a) $\frac{d}{dt}\left[r(t)\cdot u(t)\right]$ and (b) $\frac{d}{dt}\left[r(t)\times u(t)\right]$ in two different ways.

(i) Find the product first, then differentiate.

(ii) Apply the properties of Theorem 12.2.

$r(t)=ti+2t^{2}j+t^{3}k,u(t)=t^{4}k$