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Further expanding d[xy]/dx in the output of a Dt calculation

• To: mathgroup at smc.vnet.net
• Subject: [mg112984] Further expanding d[xy]/dx in the output of a Dt calculation
• From: John Accardi <accardi at accardi.com>
• Date: Sat, 9 Oct 2010 06:34:55 -0400 (EDT)

  Hello ... any help appreciated ....

Ref:

http://www.accardi.com/ImplicitDifferentiationForumQuery.nb

As you see in the *.nb cited above, during the implicit differentiation 
calculation, Mathematica includes d[xy]/dx in the solution.  I would 
like the product differentiation rule invoked for a complete 
differentiation during the Dt calculation.  Then, I would hope to see 
d[xy]/dx not show in the value of dy/dx in the Solve output.

Here it is in ASCII, but it might be easier to see if you run the 
notebook ....

eq5 = x^3-x^2y+2xy^2 == 12
Dt[eq5,x]
-3x^2 dy/dx +3x^2 + 4xy dxy/dx -6xy = 0
Solve[%%,dy/dx]
{{dy/dx -> (3x^2 + 4xy dxy/dx -6xy)/3x^2}}


How can I get Mathematica to show a more complete differentiation by 
expanding dxy/dx?


Thank you
Gianni