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Math Help - differentiation exponental by parts

  1. #1
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    differentiation exponental by parts

    Hi all

    I need to differentiate some 'complex' function and would like someone to check whether or not I did this right. I have no one to ask.
    x is parameter. The rest are constant.
     \frac{d}{dx}( -q y e^{-x y} (e^{-x y} - b)^{-1})
    = -q y e^{-x y} (-1) (e^{-x y} - b)^{-2}(e^{-x y}) (-y) - q y (e^{-x y} - b)^{-1} e^{-x y} (-y)
    =-\frac{qy^2 e^{-2xy}}{(e^{-x y} - b)^{2}} + \frac{qy^2 e^{-xy}}{e^{-x y} - b}
    =- (\frac{qy^2 e^{-2xy}}{(e^{-x y} - b)^2} - \frac{qy^2 e^{-xy}(e^{-x y} - b)}{(e^{-x y} - b)^{2}})
    =- (\frac{qy^2 e^{-xy}b}{(e^{-x y} - b)^2}})
    Last edited by avisccs; November 17th 2013 at 03:19 AM.
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  2. #2
    MHF Contributor
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    Re: differentiation exponental by parts

    Hey avisccs.

    If you want to check results that are symbolic, I would recommend you use Wolfram Alpha. For your result we get an exact confirmation of your answer (to be correct):

    d/dx (-q*y*exp(-x*y)*(exp(-x*y)-b)^(-1)) - Wolfram|Alpha
    Thanks from avisccs
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