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