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

*To*: mathgroup at smc.vnet.net*Subject*: [mg114475] Re: How to use "Apply" to do differentiation ?*From*: Patrick Scheibe <pscheibe at trm.uni-leipzig.de>*Date*: Sun, 5 Dec 2010 21:52:38 -0500 (EST)

Hi, > I have been using Mathematica for several years and > never found that. and you never questioned what Apply really does? It "replaces the head of an expression". So lets look on your expression In[8]:= FullForm[x^5] Out[8]//FullForm= Power[x,5] The head is Power. So what do we expect from Apply[D[#, x] &, x^5]? We expect that it evaluates to D[#, x] &[x,5] Since the # in your function is short for #1 this reduces to D[x,x] which is 1 (no matter what the exponent is). To investigate in this behavior, you could have replaced the normal D[..] function with something that doesn't do anything and you would have seen what happened earlier: In[15]:= Apply[d[#,x]&,x^5] Out[15]= d[x,x] Hope this helps. Cheers Patrick On Sat, 2010-12-04 at 06:16 -0500, 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? >