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Math Help - Gradient

  1. #1
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    Gradient

    Find gradient f at the given point.

    f(x,y,z)= ( (x^2+y^2+z^2)^(-1/2) ) + ln(xyz) , (-1,2,-2)

    df/dx = -x/(x^2+y^2+z^2)^(3/2)
    df/dy = -y/(x^2+y^2+z^2)^(3/2)
    df/dz = -z/(x^2+y^2+z^2)^(3/2)

    ok so after finding the partials with respect to x,y,z and plugging in the point I get the answer

    -1/27 i - 2/27 j + 2/27 k

    the books answer is

    -26/27 i +23/54 j -23/54 k
    Can anyone verify which answer is correct?
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  2. #2
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    Did you forget to take the partial derivatives of \ln(xyz)?
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  3. #3
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    Quote Originally Posted by drumist View Post
    Did you forget to take the partial derivatives of \ln(xyz)?
    I thought the partial derivative of ln(xyz) is 0 with respect to all variables?
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  4. #4
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    Nope.

    \frac{\partial}{\partial x} \ln(xyz) = \frac{yz}{xyz} = \frac{1}{x}
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  5. #5
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    Quote Originally Posted by drumist View Post
    Nope.

    \frac{\partial}{\partial x} \ln(xyz) = \frac{yz}{xyz} = \frac{1}{x}
    O yes. Thanks
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