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