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A log derivative

  1. Nov 24, 2015 #1
    1. The problem statement, all variables and given/known data

    f(c,l) = log(c - ψ(1-l)^θ )

    What is the derivative of this function wrt. l and c?


    2. Relevant equations

    I know that the derivative of log (x) = 1/x

    3. The attempt at a solution

    I got wrt c:

    1/ c - ψ(1-l)θ

    and wrt l: θψ(1-l)^θ-1 / c - ψ(1-l)^θ
     
  2. jcsd
  3. Nov 24, 2015 #2

    RUber

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    Remember the chain rule.
    ##\frac{d}{dt} f(g(t)) =f'(g(t)) * g'(t). ##
    If log is your f, and the stuff inside is your g, your first part, f'(g) would be ##\frac{1}{c-\psi (1-l)^\theta}##. Then you will need to multiply by the derivative of g wrt. whichever variable you are looking at.

    edit: This may very well be what you did, but without proper parentheses, I can't tell.
     
  4. Nov 24, 2015 #3
    Thak you. Yes, that is wahrt I did.
     
  5. Nov 24, 2015 #4

    Ray Vickson

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    Those are wrong: you should not be getting
    [tex] f_c(c,l) = \frac{1}{c} - \psi(1-l) \theta [/tex]
    which is exactly what you wrote.
     
  6. Nov 24, 2015 #5
    Yeah. I messed up the paranthesis. Thanks for telling me what I should not be getting though
     
  7. Nov 24, 2015 #6

    Ray Vickson

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    Well, maybe with proper parentheses, and fixing up ##(1-l)^{\theta}##, your result could be correct. It would be a shame to lose marks on an assignment by not using parentheses when it really takes little extra time.
     
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