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/http://calc3.askbot.com/question/95/can-we-write-used-wolfram-alpha-as-work/I've been struggling to solve a system of 3 equations (for the optimization hw) for the past 2 hours, and I just can't seem to crack it. I've found every other critical point I need to, and this is essentially the last part I need. I have even used Wolfram Alpha to solve the equations, and have verified that the answers Wolfram Alpha gives are indeed the correct answers, and the solution to the system of equations that acts as a critical point, and my Absolute Minimum. If I write the before and after, and verify that it works, can I just put down "Used Wolfram Alpha" as my inbetween steps? The assignment sheet does say we can use a computer to solve equations...I'm just worried my solution won't be "clearly written and understandable by my fellow classmates." WesTue, 15 Jul 2014 11:50:07 -0500http://calc3.askbot.com/question/95/