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Multi-variable differential question

  1. Jun 2, 2012 #1
    1. The problem statement, all variables and given/known data

    F = 1/2.a(T-Tc)M^2 + 1/4.bM^4

    I need to find dF/dM

    a,Tc,b are positive constants

    2. The attempt at a solution

    I assume this is to do with partial derivatives etc.

    So I found:

    ∂F/∂T = 1/2.aM^2

    ∂F/∂M = TaM - TcaM + bM^3

    And using a chain rule:

    dF/dM = ∂F/∂T.dT/dM + ∂F/∂M.dM/dM

    But not sure how to find dT/dM
     
    Last edited: Jun 2, 2012
  2. jcsd
  3. Jun 2, 2012 #2

    LCKurtz

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    Is that supposed to be$$
    F=(\frac 1 2)a(T-T_c)M^2 +(\frac 1 4)bM^4$$
    The statement of the problem says find ##\frac{dF}{dM}##. Isn't the expression just a polynomial in ##M##? Hold everything else constant and differentiate it.
     
  4. Jun 2, 2012 #3
    Yes that's the correct equation.

    Isn't T also a variable or have I just forgotten how to do basic differentiation?
     
  5. Jun 2, 2012 #4

    LCKurtz

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    You said it was a constant above. And if it weren't, you would still calculate the partial derivative ##\frac{\partial F}{\partial M}## the same way.
     
  6. Jun 2, 2012 #5
    Sorry, Tc is a constant but not T.

    I can see the partial derivative would hold everything else constant, but I need to find the total derivative dF/dM.
     
  7. Jun 2, 2012 #6

    LCKurtz

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    I guess I misunderstood what you wanted. If T depends on M, then the chain rule in your original post would be correct. But without more information, I don't see you you could calculate ##\frac{dT}{dM}##.
     
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