Understanding the Dot Product of Derivatives

teeeeee
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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 :-p

teeeeee
 
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teeeeee said:
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?
 
I believe Cristo meant evaluating
\frac{d}{dt}\left(\frac{dr}{dt}\cdot\frac{dr}{dt}\right)
 
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