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Re: Derivative


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 





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