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Simplifying this differential using product rule?

  1. Mar 12, 2012 #1
    Hi, I am trying to simplify this;

    [tex]
    x \frac{\partial}{\partial x} W(x,y) - \frac{\partial}{\partial x} (xW(x,y))

    [/tex]

    Am I correct in thinking I can do this with the product rule, as;

    [tex]

    \frac{\partial}{\partial x} (xW(x,y)) = \left( \frac{\partial x}{\partial x}\right) W(x,y) + x \frac{\partial W(x,y)}{\partial x}

    \\

    =W(x,y) + x \frac{\partial W(x,y)}{\partial x}

    [/tex]

    Giving the whole thing as;

    [tex]

    x \frac{\partial W(x,y)}{\partial x} - W(x,y) - x \frac{\partial W(x,y)}{\partial x}=W

    [/tex]

    Is this correct??

    Thanks
     
  2. jcsd
  3. Mar 12, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi climbon! :wink:
    yes! :smile:
     
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