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

• To: mathgroup at smc.vnet.net
• Subject: [mg114460] Re: How to use "Apply" to do differentiation ?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 5 Dec 2010 21:49:53 -0500 (EST)

Why are you surprised at the result? Recall that what Apply[fn, expr] 
does is to replace Head[expr] by fn and then evaluate that.

For simplicity, let's use the name:

   d = D[#, x] &

Now Head[x^5] is Power, so the result from Apply[d, x^5] is the same (as 
your trace will show you) as that from D[x,x], which is of course 1.

I presume the whole point of what you were doing was to use a name for 
the first-derivative operator.  Why not just the following?

   d[x^5]

On 12/4/2010 6:16 AM, 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?
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
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