Re: Partial derivative function definitions

• To: mathgroup at smc.vnet.net
• Subject: [mg127544] Re: Partial derivative function definitions
• From: "Mat' G\." <ellocomateo at free.fr>
• Date: Fri, 3 Aug 2012 04:15:40 -0400 (EDT)
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```2012-08-02 10:54, Mat' G. scripsit:
> Hello,
> Can someone please explain me why the following partial derivative
> function definitions do not work? I get errors like:
> General::ivar: -6.28229 is not a valid variable. >>
> General::ivar: -5.38469 is not a valid variable. >>
> General::ivar: -4.48709 is not a valid variable. >>
> General::stop: Further output of General::ivar will be suppressed during
> this calculation. >>
>
> Thanks for helping!
> Mat
>
>
>
>
> XFunction[x_, y_] := Sin[x] Sin[y];
> YFunction[x_, y_] := Cos[x] Cos[y];
> dXFunctiondx[x_, y_] := D[XFunction[x, y], x];
> dXFunctiondy[x_, y_] := D[XFunction[x, y], y];
> dYFunctiondx[x_, y_] := D[YFunction[x, y], x];
> dYFunctiondy[x_, y_] := D[YFunction[x, y], y];
>
> Grid[{
>     {
>      DensityPlot[
>       XFunction[x, y], {x, -2 \[Pi], 2 \[Pi]}, {y, -2 \[Pi], 2 \[Pi]}]
>      , DensityPlot[
>       YFunction[x, y], {x, -2 \[Pi], 2 \[Pi]}, {y, -2 \[Pi], 2 \[Pi]}]
>      }
>     , {
>      DensityPlot[
>       dXFunctiondx[x, y], {x, -2 \[Pi], 2 \[Pi]}, {y, -2 \[Pi], 2 \[Pi]}]
>      , DensityPlot[
>       dYFunctiondx[x, y], {x, -2 \[Pi], 2 \[Pi]}, {y, -2 \[Pi], 2 \[Pi]}]
>      }
>     , {
>      DensityPlot[
>       dXFunctiondy[x, y], {x, -2 \[Pi], 2 \[Pi]}, {y, -2 \[Pi], 2 \[Pi]}]
>      , DensityPlot[
>       dYFunctiondy[x, y], {x, -2 \[Pi], 2 \[Pi]}, {y, -2 \[Pi], 2 \[Pi]}]
>      }
>     }]
>
Thank you David Park for providing the answer: replacing the SetDelayed
for the derivative function by Set! It does work now.

I can plot the derivative, but I get a very poor resolution, that I
cannot improve with MaxRecursion. Can anyone help me understand why
please? How can I improve the derivative graphs resolution? My current
file is to be found on:

http://www.sendspace.com/file/haksg8

Thanks for helping!

```

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