# Dot Product of Derivatives

1. Oct 9, 2009

### teeeeee

Hi,
Im having trouble understanding something in one of my Dynamics lectures.
The lecturer said that:

dr/dt dotted with d2r/dt2 (where r is a vector)

equals: (1/2)(d/dt(dr/dt dotted with dr/dt))...

I just cant get this result. I know it has something to do with the product rule.

Thanks for your help, and sorry for the crudity of my notation

teeeeee

2. Oct 9, 2009

### cristo

Staff Emeritus
It does. Have you tried evaluating $$\frac{dr}{dt}\cdot\frac{dr}{dt}$$ using the product rule? What do you get?

3. Oct 9, 2009

### HallsofIvy

Staff Emeritus
I believe Cristo meant evaluating
$$\frac{d}{dt}\left(\frac{dr}{dt}\cdot\frac{dr}{dt}\right)$$