http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Thu, 17 Jul 2014 12:21:25 -0500http://calc3.askbot.com/question/126/partial-derivative/So with the function $$f(x,y)=\frac{x^{2}-y}{y^{2}-x}$$ I don't like the quotient rule because it seems like it makes way more sense to just find$$\frac{\partial}{\partial x}(x^{2}-y)(y^{2}-x)^{-1}$$$$=2x(y^{2}-x)+(-1)(y^{2}-x)^{-2}(-1)$$ $$=2x(y^{2}-x)+(y^{2}-x)^{-2}$$ But wolfram alpha is getting $$\frac{x^{2} -2xy^{2}+y}{(x-y^{2})^{2}}$$ I've tried jumping through a bunch of algebra hoops to see if my answer can be simplified to its but I can't pull it off. Is my answer somehow wrong or is Wolfram doing some weird simplification that I can't do?SpaceManSpiffThu, 17 Jul 2014 12:21:25 -0500http://calc3.askbot.com/question/126/