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How to differentiate an equation

  1. Nov 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Hi Everyone,

    This seems like a very simple question but I' a bit confused.

    In maths if I wanted to differentiate y = x^2 then it would just be 2x but I'm not sure about what you would do in physics. If you had the equation C = m/V (Concentration = mass/volume) how can you differenicate that with respect to time or something?
    2. Relevant equations


    3. The attempt at a solution
    Surely what ever type of differentiation you did (normal, partial etc.) all the parts would just end up being 0 so the differential is zero.

    Can someone please set me straight.

    Thanks,
     
  2. jcsd
  3. Nov 23, 2014 #2

    mfb

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    Staff: Mentor

    If you calculate the derivative with respect to x.
    Do m or V depend on time?
    If yes (how?), you have to take this into account. Simple example: m=c*t with some constant t leads to a non-zero time derivative.
    If no, they are just constants.
     
  4. Nov 25, 2014 #3

    rude man

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    Your example:
    C = mV-1
    dC = ∂C/∂m dm + ∂C/∂V dV
    so dC/dt = ∂C/∂m dm/dt + ∂C/∂V dV/dt.
    But ∂C/∂m = 1/V and ∂C/∂V = -m/V2
    So if you know how m and V vary with time you can compute dC/dt.
     
    Last edited: Nov 26, 2014
  5. Nov 25, 2014 #4
    You differentiate it using the quotient rule:

    [tex]\frac{dC}{dt}=\frac{V\frac{dm}{dt}-m\frac{dV}{dt}}{V^2}=\frac{\frac{dm}{dt}-C\frac{dV}{dt}}{V}[/tex]

    Chet
     
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