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Time derivatives where there's no explicit time dependence

  1. Mar 18, 2007 #1


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    Say I have a funciton sin(theta - phi)

    theta and phi are both time-dependant. How do I take the time derivative of this function? Is there a general notation or do I have to assume theta = w1t and phi = w2t and go with that?
  2. jcsd
  3. Mar 18, 2007 #2


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    You use the multivariate chain rule:

    [tex]\frac{d}{dt}f(\theta,\phi) = \frac{\partial f}{\partial \theta}\frac{d \theta}{dt} + \frac{\partial f}{\partial \phi}\frac{d \phi}{dt}[/tex]

    Of course, you do then need to know the time derivatives of theta and phi. (Note that this also assumes theta and phi are functions of time only).
  4. Mar 18, 2007 #3


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    ah, thank you much, that's exactly what I was looking for.
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