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Aerospace Math help

  1. Jul 25, 2009 #1
    Can someone please explain the steps to derive this? I've seen it everywhere, but the explanation is never given.

    My confusion arises from the second line. In EVERY math book I've ever picked up, whenever you take a derivative, it is ALWAYS with respective to something, i.e y w.r.t x, or some variable w.r.t time, etc. But in this example as shown in textbooks, it seems as though they are taking a derivative, but it is not w.r.t anything. For example, instead of saying dy/dx, they would just be saying dy, which doesn't really make any sense to me. I'm confused about this.

    I haven't seen a good explanation of this type of derivative yet. I attached an example. Thanks

    Attached Files:

    • eq.png
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  2. jcsd
  3. Jul 25, 2009 #2
    It's just a differential area. You have not paid close enough attention to your math books. :wink:
    Last edited: Jul 25, 2009
  4. Jul 26, 2009 #3


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    Look up the product rule for derivatives. The dot implies the time derivative. Since all terms on both sides are wrt dt it cancels out.
  5. Jul 26, 2009 #4
    Could you maybe say a little bit more about that. I think this is the part that is confusing me.
  6. Jul 26, 2009 #5
    It's a differential, it's not a derivative.
  7. Jul 26, 2009 #6


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    Hi mfc5200! :wink:

    Does this help … http://en.wikipedia.org/wiki/Differential_(infinitesimal) ? :smile:
  8. Jul 26, 2009 #7

    m-dot =pVA
    d(m-dot)/dt = pV dA/dt + VA dp/dt + pA dV/dt
    Now multiply both sides by dt.
  9. Jul 30, 2009 #8
    Yea, I was able to get that far. I just wasn't sure if you were "allowed" to do that. I've never seen that done before.
  10. Jul 30, 2009 #9
    You're not always allowed to do this. So, be aware of that.
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