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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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