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

• To: mathgroup at smc.vnet.net
• Subject: [mg114510] Re: How to use "Apply" to do differentiation ?
• From: Albert Retey <awnl at gmx-topmail.de>
• Date: Sun, 5 Dec 2010 21:59:05 -0500 (EST)
• References: <idd7ts$nja$1@smc.vnet.net>

Hi,

> 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.

I think your expectation of what Apply does is fooling you. Apply is
doing what it is supposed: it replaces the Head Power in Power[x,5] with
Function[D[#,x]], and since # is #1 will evaluate D[x,x], not even
looking at the second argument.

> Finally I have to take a detour and use:
> Nest[D[#, x] &, x^5, 1]

You could also just have done:

(D[#, x] &)[x^5]

> I have been using Mathematica for several years and
> never found that. I myself is wordless, but can anyone
> explain that?

hth,

albert