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Math Help - Chain rule and disagreement with the book's answer.

  1. #1
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    Mar 2010
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    Chain rule and disagreement with the book's answer.

    The exercise states: "Find dz/dt using the chain rule"
    F(x,y) = xLny + yLnx, x=t+1 y=Lnt

    My answer:
    (Lny+(x/y)) + (Lnx + (y/x))*(1/t)

    Book's answer:
    (Lny+(y/x)) + (Lnx + (x/y))*(1/t)

    I donīt understand why they inverse the x/y division. Could any one help me please? :S
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  2. #2
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    May 2010
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    f_x=\ln y+\dysplaystyle\frac{y}{x}

    f_y=\dysplaystyle\frac{x}{y}+\ln x

    x_t=1

    y_t=\dysplaystyle\frac{1}{t}

    Then the chain rule gives:
    (\ln y+\dysplaystyle\frac{y}{x},\dysplaystyle\frac{x}{y  }+\ln x)*(1,\dysplaystyle\frac{1}{t})= (*) is the dot product.

    =\ln y+\dysplaystyle\frac{y}{x}+(\dysplaystyle\frac{x}{  y}+\ln x)(\dysplaystyle\frac{1}{t})
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