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A simple calculus question

  1. Sep 25, 2005 #1
    i just want simple explanation of this.
    velocity v is a function of r and t.
    then my professor, in order to derive relationship of something, he wrote:
    [tex]\frac{dv}{dt}=\frac{\partial v}{\partial r}+\frac{\partial v}{\partial t}[/tex]
    then assuming small spatial variation,
    [tex]\frac{dv}{dt} \approx \frac{\partial v}{\partial t}[/tex]
    my question: is the first equation above OK?
    is it standard calculus? i am weak in this. please help.

  2. jcsd
  3. Sep 25, 2005 #2
    look up the chain rule; when v = v(r(t),t),

    [tex]\frac{dv}{dt}=\frac{\partial v}{\partial r}\frac{dr}{dt}+\frac{\partial v}{\partial t}[/tex]

    then you can see the following argument makes more sense?
  4. Sep 25, 2005 #3
    thanks. i just want to clarify again, does it mean dr/dt is small, i.e. small velocity?
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