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Re: Anomaly? or at least a surprise.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90296] Re: Anomaly? or at least a surprise.
  • From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Fri, 4 Jul 2008 04:01:49 -0400 (EDT)
  • References: <g4i942$3cr$1@smc.vnet.net>

Steve Gray <stevebg at roadrunner.com> wrote:
> Doing D[ArcTan[x], x] gives 1/(x^2+1) as expected.
> Doing Plot[D[ArcTan[x]],{x,-10,10},PlotRange->Full] with no variable
> to differentiate by gives a correct plot (!) This is surprising - Help
> says nothing about leaving out the independent variable even when the
> function is of only one variable. Now, doing
> Plot[D[ArcTan[x], x], {x, -10, 10}, PlotRange -> Full]
> gives error messages such as
>
> General::ivar: -9.18326 is not a valid variable. >>
> General::ivar: -9.59143 is not a valid variable. >>, etc.
>
> I thought that D[ArcTan[x], x] and 1/(x^2+1) should behave identically
> in the Plot statement.

If you Evaluate D[ArcTan[x] first, then you do get identical behavior:

Plot[Evaluate[D[ArcTan[x], x]], {x, -10, 10}, PlotRange -> Full]

Look at the first few items of "More Information" in the documentation for
Plot.

David


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