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Thread: Help with proving Young's Theorem and a derivative involving e

  1. #1
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    Help with proving Young's Theorem and a derivative involving e

    f(x1,x2,x3 )= x21e(3x2+x1x3)+(2x32/x1)

    Show that f12=f21 and f13=f31, which are implications of Young's Theorem.

    What I did was FOCs with regards to x1,x2,x3. So I ended up with;

    df/dx1= 2x1e(3x2+x1x3) -2x2^3/x1^2

    df/dx2= 3x2e(3x2+x1x3) +6x2^2/x1


    df/dx3=x31e(3x2+x1x3)

    ....After many attempts I was unsuccessful at cracking the code. The solution guide states:

    f12=f21= (6x1+3x21x3)e(3x2+x1x3)-6x22/x21


    f13=f31= (3x21+x31x3)e(3x2+x1x3)

    If anyone could fully explain this to me, I would really appreciate it because I am very perplexed as to how they logically came up with the answer. Thank you very much.
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  2. #2
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    Re: Help with proving Young's Theorem and a derivative involving e

    It looks like you are having problems interpreting notation.

    $\displaystyle f_{12} = {\partial \over \partial x_2}\left({\partial f \over \partial x_1}\right)$
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  3. #3
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    Re: Help with proving Young's Theorem and a derivative involving e

    What is "FOCs"??
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  4. #4
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    Re: Help with proving Young's Theorem and a derivative involving e

    First order conditions.
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