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Math Help - Find all 2nd partial derivatives

  1. #1
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    Find all 2nd partial derivatives

    xy/(x-y)

    New concept and I'm having trouble with ones that are not linear equations. Could someone help me out?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sfgiants13 View Post
    xy/(x-y)

    New concept and I'm having trouble with ones that are not linear equations. Could someone help me out?
    linear, non-linear, makes little difference. you want to find \frac {\partial ^2 f}{\partial x ^2} and \frac {\partial ^2 f}{\partial y^2} for f(x,y) = \frac {xy}{x - y}

    to find the first, differentiate with respect to x twice. that is, treat y as a constant. so you would just differentiate normally thinking of y as just any other number, like 2 or something.

    a similar approach can get you \frac {\partial ^2 f}{\partial y^2}

    can you start?
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jhevon View Post
    linear, non-linear, makes little difference. you want to find \frac {\partial ^2 f}{\partial x ^2} and \frac {\partial ^2 f}{\partial y^2} for f(x,y) = \frac {xy}{x - y}

    to find the first, differentiate with respect to x twice. that is, treat y as a constant. so you would just differentiate normally thinking of y as just any other number, like 2 or something.

    a similar approach can get you \frac {\partial ^2 f}{\partial y^2}

    can you start?
    Don't forget about \frac{\partial^2f}{\partial x\partial y} and \frac{\partial^2f}{\partial y\partial x}!!!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Don't forget about \frac{\partial^2f}{\partial x\partial y} and \frac{\partial^2f}{\partial y\partial x}!!!
    i didn't forget. uh, i was just seeing if you were paying attention. gotta keep you on your toes
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