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Math Help - Partial Derivatives....help!

  1. #1
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    Partial Derivatives....help!

    Calculate all second derivatives for v = xy/(x-y)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by leungsta View Post
    Calculate all second derivatives for v = xy/(x-y)
    i will do \frac {\partial v}{\partial x} and \frac {\partial^2 v}{\partial x^2}, the partial derivatives with respect to y are similar.

    when taking the partial derivatives with respect to x, you treat all other variables as constants. so my y's might as well be 2's now

    thus, by the quotient rule: \frac {\partial v}{\partial x} = \frac {(x - y)y - xy}{(x - y)^2} = \frac {-y^2}{(x - y)^2} = -y^2 (x - y)^{-2}

    thus, by the chain rule, \frac {\partial^2 v}{\partial x^2} = \frac {\partial}{\partial x} \left( \frac {\partial v}{\partial x} \right) = 2y^2(x - y)^{-3}
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by leungsta View Post
    Calculate all second derivatives for v = xy/(x-y)
    Did you first compute \frac{\partial v}{\partial x}, \frac{\partial v}{\partial y}??

    --Chris
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    Did you first compute \frac{\partial v}{\partial x}, \frac{\partial v}{\partial y}??

    --Chris
    Nope I tried doing the first partial derivative but wasn't sure how to do it
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