       Re: repost - expanding inline d[xy]/dx during implicit

• To: mathgroup at smc.vnet.net
• Subject: [mg113179] Re: repost - expanding inline d[xy]/dx during implicit
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 16 Oct 2010 13:13:47 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```xy is a separate symbol not the product of x and y.  Add a space or an explicit times, i.e., x*y

Bob Hanlon

---- John Accardi <accardi at accardi.com> wrote:

=============
Thanks in advance for any help .....

Implicit Differentiation

Below, I need to get the inline d[xy]/dx to expand in the Dt output.
Ditto for the output of Solve.  (I have done other implicit differentiation
calculations that have done this correctly.) What is the issue here?

eq5=x^3-3x^2 y+2xy^2==12

x^3-3 x^2 y+2 xy^2\[LongEqual]12

Dt[eq5,x]

-3 x^2 \[DifferentialD]y/\[DifferentialD]x+3 x^2+4 xy
\[DifferentialD]xy/\[DifferentialD]x-6 x y\[LongEqual]0

Solve[%%,\[DifferentialD]y/\[DifferentialD]x]

{{\[DifferentialD]y/\[DifferentialD]x->(3 x^2+4 xy
\[DifferentialD]xy/\[DifferentialD]x-6 x y)/(3 x^2)}}

*.nb is located here:

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

Thanks,
Gianni

```

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