D/dt |r(t)| = (1/|r(t)|) r(t)dot r'(t)

[calorimetry]

Homework Statement

If vector r(t) is not 0, show that d/dt |r(t)| = (1/|r(t)|) r(t)dot r'(t).

The last part is the dot product of r(t) and r'(t).

Homework Equations

The hint given was that |r(t)|^2 = r(t) dot r(t)

The Attempt at a Solution

Not sure where to begin, but I thought that |r(t)| is the length or magnitude of the vector r(t), thus its derivative is zero. If this is correct, then I also need to prove that the right side = zero.

 

[Office_Shredder]

Depending on what r(t) is, surely it's magnitude can change over time?

Can you take the derivative of both sides of the equation in the hint using the chain rule?

 

[calorimetry]

Thanks for the hint on the hint. So simple and I didn't see it before.