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Anomaly? or at least a surprise.

• To: mathgroup at smc.vnet.net
• Subject: [mg90250] Anomaly? or at least a surprise.
• From: Steve Gray <stevebg at roadrunner.com>
• Date: Thu, 3 Jul 2008 06:12:47 -0400 (EDT)

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

• Follow-Ups:
  • Re: Anomaly? or at least a surprise.
    • From: "W_Craig Carter" <ccarter@mit.edu>
  • Re: Anomaly? or at least a surprise.
    • From: "Curtis F. Osterhoudt" <cfo@lanl.gov>
  • Re: Anomaly? or at least a surprise.
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>