       Defining derivatives

• To: mathgroup at smc.vnet.net
• Subject: [mg84484] Defining derivatives
• From: KF <fresl at grad.hr>
• Date: Sat, 29 Dec 2007 02:55:22 -0500 (EST)

```(I am sorry if this or similar question was already answered. I did
archive search, but didn't find anything.)

I have a function:

QuarticSpline[x_] :=
Module[
{ r },
r = Abs[x];
If [r > 1.0,
0.0,
1 + r r (-6 + r (8 - 3 r))
]
]

It's first derivative should be (at least for my purposes :o) :

QuarticSplineD1 [x_] :=
Module[
{ r },
r = Abs [x];
If [r > 1.0,
0.0,
Sign[x] * r (-12 + (24 r - 12))
]
]

but D[QuarticSpline[x], x] returns

If[Abs[x] > 1., 0, 0]

Now, Mathematica Tutorial, in chapter Defining Derivatives, says

"You can define the derivative in Mathematica of a function f of one
argument simply by an assignment like f'[x_]=fp[x]."

But if I try to write

QuarticSpline'[x_] = QuarticSplineD1[x]

I got

Set::write: "Tag Function in (If[Abs[#1]>1.,0,0]&)[x_] is Protected."

Is it possible to define QuarticSpline' to "return" QuarticSplineD1 ?

Regards,

K. Fresl

```

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