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

*To*: mathgroup at smc.vnet.net*Subject*: [mg114470] Re: How to use "Apply" to do differentiation ?*From*: Chenguang Zhang <alix.zhang at gmail.com>*Date*: Sun, 5 Dec 2010 21:51:43 -0500 (EST)

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? > > >