Re: How to use "Apply" to do differentiation ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg114452] Re: How to use "Apply" to do differentiation ?*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Sun, 5 Dec 2010 21:48:27 -0500 (EST)*References*: <idd7ts$nja$1@smc.vnet.net>

Am 04.12.2010 12:16, schrieb Mayasky: > Something simple yet unbelievable occurred when I use: > > Apply[D[#, x]&, x^5] > > The output is invariably 1 whether I use x^5 or x^100. > Also I suggest you to try "Trace" command to see > the weirdness -- the output is messy if pasted as > text here. > > Finally I have to take a detour and use: > Nest[D[#, x]&, x^5, 1] > > I have been using Mathematica for several years and > never found that. I myself is wordless, but can anyone > explain that? > Its very easy to trace unexpected evaluation results Trace[D[#, x] & @@ (x^5)] // FullForm FullForm[{HoldForm[(D[#1, x] & ) @@ (x^5)], HoldForm[(D[#1, x] & )[x, 5]], HoldForm[D[x, x]], HoldForm[1]}] which is the correct formal answer, because Power[x,5] is a function of two variables. Of cause, one can doubt, if an automatic application rule for diffentiating sequences of variables without any function head is a useful concept. It is comparable to a concept of differentiating tensor products of spaces with respect to position by replacing a factor space V at position i in V_1 \times ... \times V_i \times ... by the one-dimensional spaces of multiples of the field unit 1. -- Roland Franzius