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Math Help - Partial differentiation

  1. #1
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    Partial differentiation

    How do I do the partial differentiation of following:

    F(x,y)=(1-e^-x)(1-e^-y)

    they has answer of e^-(x+y)
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Judi View Post
    How do I do the partial differentiation of following:

    F(x,y)=(1-e^-x)(1-e^-y)

    they has answer of e^-(x+y)
    The partial derivative with respect to what variable?

    (del F)/(del x) = e^{-x} * (1 - e^{-y}) <--- This is the partial derivative of F(x,y) wrt x.

    (del F)/(del y) = (1 - e^{-x}) * e^{-y} <--- This is the partial derivative of F(x,y) wrt y.

    neither of which is e^-(x+y). I'm not sure what you are asking for.

    -Dan
    Last edited by topsquark; September 22nd 2006 at 07:05 PM. Reason: Fixed a sign error
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Judi View Post
    d^2
    ----- F(x,y)=e^(-(x+y))
    dx dy

    I am trying to see how this is possible, how the left hand side is equal to the right hand side

    Thank you,
    Ah! I didn't look at second derivatives. Okay, we can do this two ways:
    (del F)/(del x) = e^{-x} * (1 - e^{-y}) (Apparently I missed a minus sign in my original response. I'll fix it.)

    So taking del/(del y) of this:
    (del^2 F)/(del x del y) = e^{-x}*e^{-y} = e^{-x - y}

    or
    (del F)/(del y) = (1 - e^{-x}) * e^{-y}

    So taking del/(del x) of this:
    (del^2)/(dex y del x) = e^{-x}*e^{-y} = e^{-x - y}

    If you are having a problem doing the partial derivatives, remember that when you do a "del/(del x)" you hold all variables other than x constant. So, for example in (del F)/(del x) we hold the y constant, so effectively we are taking the derivative of (1 - e^{-x})* constant = e^{-x}*constant.

    If you need more help than that with the derivatives, just let me know and I'll work up a quick tutorial for you.

    -Dan
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    Thank you, thank you, thank you
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Judi View Post
    Thank you, thank you, thank you
    You're welcome welcome welcome!

    -Dan
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