       RE:? D[f,{x,n}]

• To: mathgroup at smc.vnet.net
• Subject: [mg25559] RE:[mg25495] ? D[f,{x,n}]
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Sat, 7 Oct 2000 03:36:07 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Jack Goldberg had trouble making it so
D[f, x]   and   D[f, {x, n}]
perform some "simplification" on (f)
before the built in D is used.

I give some code below that does this.
Notice if you do these examples without
changing D you get factored polynomials.

Since I don't give a rule for D[f, {x, n}] this
seems to prove that D[f, {x, n}]  evaluates
Nest[ D[#, x]&, f, n ]
or something equivalent.
-----------------------------

In:=
Unprotect[D];
flag=True;

D[f_,x_]/;flag:=
Block[{flag}, D[Expand[f],x] ]

In:=
D[(x+2)^3,x]

Out=
12 + 12*x + 3*x^2

In:=
D[(x+2)^4,{x,2}]

Out=
48 + 48*x + 12*x^2

--------------------
Notice, inside Block I didn't have to set (flag=False)
We only care that flag is not True.

--------------------
On a related note, the Help Browser says
"Derivative is generated when you apply D to a function
whose derivative Mathematica does not know."  We see Derivative
in the FullForm below.

In:=
f'[x] //FullForm

Out=
Derivative[f][x]

In:=
f''[x] //FullForm

Out=
Derivative[f][x]

--------------------
Regards,
Ted Ersek

Get Mathematica tips, tricks from
http://www.verbeia.com/mathematica/tips/Tricks.html

```

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