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

*To*: mathgroup at smc.vnet.net*Subject*: [mg114503] Re: How to use "Apply" to do differentiation ?*From*: Chenguang Zhang <alix.zhang at gmail.com>*Date*: Sun, 5 Dec 2010 21:57:48 -0500 (EST)

I tried to recursively apply differentiation to a normal distribution function, and before using Nest command I wanted to check if pure function worked... Now I know that I missed "{}" in my command and Apply[D[#,x]&, {x^5}] is the correct one. Thanks to all! On Sun, Dec 5, 2010 at 1:45 PM, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > On 4 Dec 2010, at 12:16, 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? > > > > I don't see anything very strange in this. Note that the full form of x^5 > is Power[x,5]. Observe that in general > > Apply[f[#] &, p[x, y]] > > f(x) > > So not Apply[D[#,x]&,Power[x,5]] will give D[x,x] which is 1. > > What I do not understand is what you actually intended to achieve. If you > wanted simply to differentiate x^5 the way to do it is > > D[#, x] &@(x^5) > > or (if you really must): > > Compose[D[#, x] &, x^5] > > 5 x^4 > > > Andrzej Kozlowski > >