Why does dr/dt · d²r/dt² equal (1/2) d/dt(dr/dt · dr/dt)?

[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 can't 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

 

[cristo]

I know it has something to do with the product rule.

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

 

[HallsofIvy]

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