       Re: Derivative

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: Derivative
• From: John Lee <lee at math.washington.edu>
• Date: Thu, 30 Jul 92 16:15:06 -0700

```Michael Trott <trott at bibliothek.th-ilmenau.de> writes:

>  I had the following behaviour:

>  Derivative[n_][F]:=FU[n]

>  Derivative[n_][G][x_]:=GU[n][x]

>  {F''[y], G''[y] }

>  Is there a reason for this ?

I'm not sure what you're asking about here; you didn't show us any output.
However, here's what happened when I gave Mma these three lines:

In:= Derivative[n_][F]:=FU[n]

In:= Derivative[n_][G][x_] := GU[n][x]

In:= {F''[y],G''[y]}

Out= {(FU)'[y], GU[y]}

Maybe you're confused by this output.  But this is what one should expect.
Let's look at what Mathematica does with In:

F''[y]  -->  Derivative[Derivative[F]][y]
(* interpretation of the input form F''[y] *)

-->  Derivative[FU][y]
(* here it used your rule for Derivative[F],
but there are no rules to tell it how to go farther *)

-->  (FU)'[y]
(* output form of the above expression *)

G''[y]  -->  Derivative[Derivative[G]][y]
(* now there's no rule for Derivative[G] by itself *)

-->  Derivative[G][y]
(* this used Mma's usual rules for multiple derivatives *)

-->  GU[y]
(* using your rule for Derivative[G][y] *)

Jack Lee
Dept. of Mathematics
University of Washington
Seattle, WA

```

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