Proof of Vectors

[MJT]

If r(t) does not equal 0, show that d/dt (abs(r(t))) = 1/abs(r(t)) * r(t) * r'(t)

 

[daon2]

This really doesn't have anything to do with vectors, it is just the chain rule. The derivative of the absolute value of x is either -1 if x<0, or +1 if x>0. It can be "neatened up" into the following formula:

\(\displaystyle \frac{d}{dx}|x| = \frac{x}{|x|}\)

Now the result follows from simply using the chain rule.