Change in an expression that I don't understand

[mkerikss]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[cepheid]

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

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

 

[mkerikss]

Thank you