d/dt (r(t) dot r(t)) = 2(r(t) dot dr/dt)

[dagr8est]

An answer key gives the following statement as part of an answer but I don't understand how this works. This is exactly how it is written in the book. I was wondering if someone could explain this to me. Any help is appreciated. (r(t) is a vector)

d/dt (r(t) dot r(t)) = 2(r(t) dot dr/dt)[/b]

 

[soroban]

Hello, dagr8est!

It's the Product Rule . . .

\(\displaystyle \frac{d}{dt}(\bf{r}\,\cdot\,\bf{r}) \;=\;\bf{r}\cdot\frac{d\bf{r}}{dt}\,+\,\frac{d\bf{r}}{dt}\cdot\bf{r} \;=\;2\bf{r}\cdot\frac{d\bf{r}}{dt}\)