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How to use "Apply" to do differentiation ?

• To: mathgroup at smc.vnet.net
• Subject: [mg114445] How to use "Apply" to do differentiation ?
• From: Mayasky <alix.zhang at gmail.com>
• Date: Sat, 4 Dec 2010 06:16:11 -0500 (EST)

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?