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How do you take the partial derivative of this monster?

  1. Feb 17, 2010 #1
    [tex]e^{10x -x^2 +4y -y^2}[/tex]

    I don't know where to start. I have a gut feeling this might require the chain rule, but I don't know how to use it on this thing. I tried doing some silly simplification which resulted in a pair of quotients and products of exponentials and tried to derive those using the quotient rule but it didn't work.

    In any case, I need to find the first and second partial derivatives. How do I go about finding them?
     
  2. jcsd
  3. Feb 17, 2010 #2
    Hey Raziel,

    Try rewriting a more general (and less messy expression) like:

    [tex]e^{10x -x^2 +4y -y^2} = e^{f(x,y)}[/tex]

    Taking the partial derivative (w.l.o.g. with respect to x) of the above expression is just taking the derivative of the expression with respect to x while holding y constant. In other words, what is,

    [tex]\frac{d}{dx}e^{f(x)}\mathrm{?}[/tex]

    If you know this piece of information, then you should be able to evaluate,

    [tex]\frac{\partial}{\partial x}e^{f(x,y)},[/tex]

    since they follow the same evaluation process.
     
  4. Feb 17, 2010 #3
    Got it, thanks.
     
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