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

*To*: mathgroup at smc.vnet.net*Subject*: [mg114538] Re: How to use "Apply" to do differentiation ?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 7 Dec 2010 06:45:43 -0500 (EST)

This is an "illusion" just as the fact that Apply[D[#, x] &, {x^1000}] works is based on an "illusion". In fact, any head that doe not evaluate will work: Apply[D[#, x] &, F[x^1000]] 1000 x^999 Apply[D[#, x] &, HoldForm[x^1000]] 1000 x^999 Apply[D[#, x] &, InputForm[x^1000]] 1000 x^999 Apply[D[#, x] &, String[x^1000]] 000 x^999 and so on... Andrzej Kozlowski On 6 Dec 2010, at 03:51, Chenguang Zhang wrote: > I tried different forms, the following three work: > Apply[D[#, x] &, FullForm[x^1000]] > Apply[D[#, x] &, HoldForm[x^1000]] > Apply[D[#, x] &, Hold[x^1000]] > > Even the reason is clear, it is still a little unnatural to me > because Apply[D[#, x] &, x^1000] is closer to mathematical language. Anyway, > people generally use D[f[x], x] instead of the Apply command, and I tried > that command because I wanted to use Nest command to do recursive > differentiation to a function (Nest did work even Apply got me confused for > a while) > > Cheers. > > On Sat, Dec 4, 2010 at 9:02 AM, Achilleas Lazarides < > achilleas.lazarides at gmx.com> wrote: > >> Trace does show you what happened: Apply replaces the head of its second >> argument by the first. In this case, it replaces Power in Power[x,5] by >> >> D[#, x] & >> >> (the second step in the trace). So if instead of D[#,x]& you had eg >> Print[#1,#2]&, it would have printed >> x5 >> because that is what Print[x,5] does. >> >> The point is that it does not give you a message to the effect that your >> anonymous function has too many arguments in the second step in the trace; >> it just silently drops the second argument. This is what anonymous functions >> in Mathematica seem to do: silently drop extra arguments (I have no idea if >> this is good, bad, neutral, accidental etc). >> >> So basically you are evaluating >> (D[#1, x] & )[x, 5] >> which drops the second argument and differentiates x. >> >> On Dec4, 2010, at 1:16 PM, Mayasky wrote: >> >> >> 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? >> >> >>