calculus

what is the 2nd derivative of:
1-xy = x-y

i get (-y-1)/(x-1) for the first

the second i know is (-y-1)/(x-1)^2 but i keep getting (0)/(x-1)^2

please show me the steps i should be taking and if possible what i did wrong

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asked by eric
  1. I would solve it for y first

    1-xy = x-y
    y - xy = x-1
    y(1 - x) = x-1
    y = (x-1)/(1-x) = -1 , x ≠1

    Well, isn't that special !!!

    so y' = 0 and of course
    y '' = 0

    Wolfram took it as a pair of intersecting lines.
    Notice the horizontal line y = -1
    The vertical line x = 1 will give us y = any real number
    e.g. (1, 4.56) will work
    LS = 1 - 1(4.56)
    RS = 1 - 4.56
    LS = RS

    http://www.wolframalpha.com/input/?i=plot+1-xy+%3D+x-y+

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    posted by Reiny

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