Partial Diff

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  1. dugdugdug's Avatar
    1 01-04-2012  03:57
    • Exalted Member
    • Posts: 374
    Partial Diff
  2. teamnoether's Avatar
    2 01-04-2012  08:29
    • Full Member
    • Posts: 116
    Re: Partial Diff
    Well, as you suggested, it's not very clear what f is supposed to be. My best guess would be that f is supposed to be z (because it was defined as a function of x and y) and that they're asking for implicit differentiation. You could also isolate z and then use a quotient rule, which would get you to the same place.

    xyz = x - y + z

    For example, if you take the partial in x you get

    yz + xy\frac{\partial z}{\partial x} = 1 + \frac{\partial z}{\partial x}

    \frac{\partial z}{\partial x} = \frac{yz - 1}{1 - xy}

    If you want to get rid of the z, you can write

    z = \frac{x - y}{xy - 1}

    and then substitute back in to get

    \frac{\partial z}{\partial x} = \frac{y^2 - 1}{(xy - 1)^2}
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