1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Change in an expression that I don't understand

  1. Oct 24, 2009 #1
    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[tex]\vec{v}[/tex]/dt*[tex]\vec{v}[/tex]=d/dt(1/2[tex]\vec{v}[/tex]*[tex]\vec{v}[/tex])

    Can someone explain?
    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 24, 2009 #2

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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

    [tex] \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} [/tex] ​
     
  4. Oct 24, 2009 #3
    Thank you:smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook