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

**References**:**Anomaly? or at least a surprise.***From:*Steve Gray <stevebg@roadrunner.com>