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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:


    Can someone explain?
    2. Relevant equations

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


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    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:
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