Partial Differentiation of Implicit Functions
- To: mathgroup at smc.vnet.net
- Subject: [mg83170] Partial Differentiation of Implicit Functions
- From: "Jay" <jay at aleka.freeserve.co.uk>
- Date: Tue, 13 Nov 2007 07:01:08 -0500 (EST)
- Organization: Helsinki Television
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.
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- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
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