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Math Help - need my work checked plz :)

  1. #1
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    need my work checked plz :)

    u= ln(sqrt(x^2+y^2))


    u(x) = x / (2sqrt((x^2+y^2))
    u(xx) = (1-2x^2)/(2(sqrt(x^2+Y^2))^3)

    u(y)= y / (2sqrt((x^2+y^2))
    u(yy)= (1-2y^2)/(2(sqrt(x^2+Y^2))^3)

    i havent done derivatives for a while now .. not sure it is correct..
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  2. #2
    Senior Member
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    you could use some of the properties of logarithms for this one:

    u = \ln(\sqrt{x^2+y^2}) = \frac{1}{2}\ln(x^2+y^2)

    so then:

    u(x) = \frac{1}{2} \times \frac{1}{x^2+y^2} \times 2x = \frac{x}{x^2+y^2}

    u(xx) = \frac{(1)(x^2+y^2) - 2x(x)}{(x^2+y^2)^2} = \frac{-x^2+y^2}{(x^2+y^2)^2}

    u(y) = \frac{1}{2} \times \frac{1}{x^2+y^2} \times 2y = \frac{y}{x^2+y^2}

    u(yy) = \frac{(1)(x^2+y^2) - 2y(y)}{(x^2+y^2)^2} = \frac{x^2-y^2}{(x^2+y^2)^2}
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