Re: Partial Differentiation of Implicit Functions
- To: mathgroup at smc.vnet.net
- Subject: [mg83277] Re: Partial Differentiation of Implicit Functions
- From: "Jay" <jay at aleka.freeserve.co.uk>
- Date: Fri, 16 Nov 2007 05:41:44 -0500 (EST)
- Organization: Helsinki Television
- References: <fhc3pe$510$1@smc.vnet.net>
Thanks guys. Seems I had got confused between the use of 'Solve' and 'Eliminate' Jay. "Jay" <jay at aleka.freeserve.co.uk> wrote in message news:fhc3pe$510$1 at smc.vnet.net... > Hi, > > I have some equations of the form: > AA x^2 + BB y^2 + CC z^2 + DD x y +EE x z + FF y z + GG x + HH y + II z + > JJ== 0 > > I want to solve for e.g. partial dy/dz = 0 and then combine the result > with > the original equation to get a new implicit equation. > > E.g. > > E1 := -2 + x^2 + x z + y^2 + z^2 > > (where I require E1 == 0) > > Manually performing the differentiation gives: > > partial dx/dz (y constant) = (x+2 z)/(2x + z) == 0 > > I can then go back into mathematica and do > > Eliminate[{E1 == 0, 2*z + x == 0}, {z}] > > giving: > > 4 x y + 4 y^2 == 8 - 5 x^2 > > This is what I want but how do I do everything in Mathematica? I expected > to > be able to do something like: > > Solve[E1==0,D[x,y]] > > but it doesn't seem to work (says "0" is not a valid variable) > > Thanks, > > Jay. > > > > > > >