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[75]:= Derivative[n_][F]:=FU[n]
In[76]:= Derivative[n_][G][x_] := GU[n][x]
In[77]:= {F''[y],G''[y]}
Out[77]= {(FU[1])'[y], GU[2][y]}
Maybe you're confused by this output. But this is what one should expect.
Let's look at what Mathematica does with In[77]:
F''[y] --> Derivative[1][Derivative[1][F]][y]
(* interpretation of the input form F''[y] *)
--> Derivative[1][FU[1]][y]
(* here it used your rule for Derivative[1][F],
but there are no rules to tell it how to go farther *)
--> (FU[1])'[y]
(* output form of the above expression *)
G''[y] --> Derivative[1][Derivative[1][G]][y]
(* now there's no rule for Derivative[1][G] by itself *)
--> Derivative[2][G][y]
(* this used Mma's usual rules for multiple derivatives *)
--> GU[2][y]
(* using your rule for Derivative[2][G][y] *)
Jack Lee
Dept. of Mathematics
University of Washington
Seattle, WA