Change in an expression that I don't understand

1. Oct 24, 2009

mkerikss

1. The problem statement, all variables and given/known data
In the answer to a homework I didn't understnad why these are the same:

d$$\vec{v}$$/dt*$$\vec{v}$$=d/dt(1/2$$\vec{v}$$*$$\vec{v}$$)

Can someone explain?
2. Relevant equations

3. The attempt at a solution

2. Oct 24, 2009

cepheid

Staff Emeritus
The product rule for differentation applies, even if it is a vector dot product that is being differentiated. Therefore:

$$\frac{d}{dt}\left(\frac{1}{2}\vec{v} \cdot \vec{v}\right) = \frac{1}{2}\vec{v}\cdot \frac{d\vec{v}}{dt} + \frac{1}{2}\frac{d\vec{v}} {dt}\cdot \vec{v}$$ ​

3. Oct 24, 2009

Thank you