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