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

*To*: mathgroup at smc.vnet.net*Subject*: [mg112996] Re: Further expanding d[xy]/dx in the output of a Dt calculation*From*: telefunkenvf14 <rgorka at gmail.com>*Date*: Sun, 10 Oct 2010 06:41:53 -0400 (EDT)*References*: <i8pghf$fit$1@smc.vnet.net>

On Oct 9, 5:35 am, John Accardi <acca... at accardi.com> wrote: > 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 Mathematica is treating 'xy' as a unique variable, not a product. Include a space between the variables OR use * to indicate multiplication in your 'eq5' and I think you'll get what you want. FYI, I looked at your notebook, and noticed you were using traditional form input and output. Everyone has their own prefs here, but my experience is that using StandardForm input/output helps you catch your mistakes, making programming much less painful!! (You can always make things pretty later...) In[1]:= eq5 = x^3 - 3 x^2 y + 2 x y^2 == 12 Dt[eq5, x] Solve[%, Dt[y, x]] Out[1]= x^3 - 3 x^2 y + 2 x y^2 == 12 Out[2]= 3 x^2 - 6 x y + 2 y^2 - 3 x^2 Dt[y, x] + 4 x y Dt[y, x] == 0 Out[3]= {{Dt[y, x] -> (3 x^2 - 6 x y + 2 y^2)/(x (3 x - 4 y))}} -RG