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Differentiation of two similar systems

  1. Nov 13, 2014 #1
    1. The problem statement, all variables and given/known data
    Hi. i need help with understanding task with differentiation.
    i have two separate tasks, and i need help understanding why the solutions differ somewhat.
    system 1:
    Y = C + I + G
    C = f(Y-T)
    I = h(r)
    r = m(M)

    system 2:
    Y = C + I + G
    C = F(Y,T,r)
    I = f(Y,r)

    in system 1. when differentiating system 1, the "C-equation", the book gives then answer f'(dY - dT),,,, the derivative is not specified to be in respect to Y or T.
    in system 2, when differentiating the C-equation", the book gives the answer: f'(Y)*dY + f'(T)*dT + f'(r)*dr
    the symbol in the parentheses are meant to tell in what respect the derivation is.
    the question is, why are the differentiating ( only of the C-equation, i know how the rest) different?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 13, 2014 #2
    found out on my own :)
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