# differentiation exponental by parts

• Nov 17th 2013, 02:45 AM
avisccs
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.
$\frac{d}{dx}( -q y e^{-x y} (e^{-x y} - b)^{-1})$
$= -q y e^{-x y} (-1) (e^{-x y} - b)^{-2}(e^{-x y}) (-y) - q y (e^{-x y} - b)^{-1} e^{-x y} (-y)$
$=-\frac{qy^2 e^{-2xy}}{(e^{-x y} - b)^{2}} + \frac{qy^2 e^{-xy}}{e^{-x y} - b}$
$=- (\frac{qy^2 e^{-2xy}}{(e^{-x y} - b)^2} - \frac{qy^2 e^{-xy}(e^{-x y} - b)}{(e^{-x y} - b)^{2}})$
$=- (\frac{qy^2 e^{-xy}b}{(e^{-x y} - b)^2}})$
• Nov 17th 2013, 03:06 PM
chiro
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