Here’s a problem (2.1.4, p. 23) from Lang’s “A Second Course in Calculus”:

Find the velocity vector of the following curve: (cos(3*t*), sin(3*t*)).

Finding the velocity vector simply requires you to take the derivative of each term. Here’s a good chance to remember the chain rule:

Therefore, the velocity vector of (cos(3*t*), sin(3*t*)) is (-3sin(3*t*), 3cos(3*t*)).

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