Re: Anomaly? or at least a surprise.

• To: mathgroup at smc.vnet.net
• Subject: [mg90298] Re: [mg90250] Anomaly? or at least a surprise.
• From: "W_Craig Carter" <ccarter at mit.edu>
• Date: Fri, 4 Jul 2008 04:02:12 -0400 (EDT)
• References: <200807031012.GAA03197@smc.vnet.net>

```Hello Steve,
A couple things to note:

D[ArcTan[x]] (*returns ArcTan[x]*)

Thus, using Evaluate:

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

Give the same plot as:

Plot[(1 + x^2)^(-1), {x, -10, 10}, PlotRange -> Full]

A quick look at the documentation for D[__] doesn't indicate that this
(D[f[x]]) should work, but I believe the output is sensible. However,
I also believe that it should throw a warning.

WCC

On Thu, Jul 3, 2008 at 6:12 AM, 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.
>
> Is this behavior something I should know? Thank you.
>
> Steve Gray
>
>

--
W. Craig Carter

```

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