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

• To: mathgroup at smc.vnet.net
• Subject: [mg113000] Re: Further expanding d[xy]/dx in the output of a Dt calculation
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Sun, 10 Oct 2010 06:42:39 -0400 (EDT)
• References: <i8pghf\$fit\$1@smc.vnet.net>

```John Accardi 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
>

It seems to me, that you missed a space between x and y. xy is not x*y
but a new variable

//Peter
--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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