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Derivative question

  1. Jan 3, 2012 #1
    I'd like to know the result of deriving both sides of the equation in respect to time

    [itex] v= \frac {V}{m} [/itex]

    [itex] \frac {d}{dt}v=( \frac {d}{dt}) \frac {V}{m} [/itex]

    which gives

    [itex] \dot v = . . . ? [/itex]

    If you want some backup, this is a very common thermodynamics relation, where V = volume, m = mass and v = specific volume [m3/kg]. In open systems, we want to know mass flow and volumetric flow so we get [itex] \dot m[/itex] [kg/s] and [itex] \dot V[/itex] [m3/s]. I'd like to know if there's such a thing about specific volume as well, and that depends on how you do that derivative.

    Best wishes and thanks,

  2. jcsd
  3. Jan 3, 2012 #2


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    Science Advisor

    The quotient rule applies: dv/dt = {mdV/dt - Vdm/dt}/m2
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