nth derivative
in [HP48]
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From: supergems on 15 Oct 2009 10:47 I wrote a simple program for calculating the nth derivative: \<< \-> F V N \<< F XQ 1 N FOR K V DERIV SIMPLIFY NEXT \>> \>> 'DERVN' STO 'Function' 'Variable' 'N' --> nth derivative Examples of use of DERVN program: '1/\v/X' 'X' 3 --> '-(15*\v/X/(8*X^4))' '\.S(-\oo,1/X,EXP(-Y^2),Y)' 'X' 2 --> '(2*X^2-2)/(X^5*EXP(1/X^2))' 'F(X,Y,Z)' 'Z' 2 --> 'd3d3F(X,Y,Z)' If I apply my DERVN program this function: 'F(X,Y)=X*Y/(X^2+Y^2)' 'Y' 2 --> "Error: Invalid User Function" Why am I getting that message? If I delete 'SIMPLIFY' then get the correct result, obviously not simplified: \<< \-> F V N \<< F XQ 1 N FOR K V DERIV NEXT \>> \>> 'DERVN' STO 'F(X,Y)=X*Y/(X^2+Y^2)' 'Y' 2 --> 'd2d2F(X,Y)=(SQ(X^2+Y^2)*(X*(2*Y)-(X* (2*Y)+2*(X*Y)))-(X*(X^2+Y^2)-X*Y*(2*Y))*(2*((X^2+Y^2)*(2*Y))))/SQ(SQ (X^2+Y^2))' then SIMPLIFY: 'd2d2F(X,Y)=-((6*Y*X^3-2*Y^3*X)/ (X^6+3*Y^2*X^4+3*Y^4*X^2+Y^6))' Cheers, Simone.
From: Damir on 15 Oct 2009 13:17 On Thu, 15 Oct 2009 07:47:27 -0700 (PDT), supergems <simone.cerica(a)gmail.com> wrote: >I wrote a simple program for calculating the nth derivative: > >\<< \-> F V N > \<< F XQ 1 N > FOR K V DERIV SIMPLIFY > NEXT > \>> >\>> 'DERVN' STO > >'Function' 'Variable' 'N' --> nth derivative > >Examples of use of DERVN program: > >'1/\v/X' 'X' 3 --> '-(15*\v/X/(8*X^4))' >'\.S(-\oo,1/X,EXP(-Y^2),Y)' 'X' 2 --> '(2*X^2-2)/(X^5*EXP(1/X^2))' >'F(X,Y,Z)' 'Z' 2 --> 'd3d3F(X,Y,Z)' > >If I apply my DERVN program this function: > >'F(X,Y)=X*Y/(X^2+Y^2)' 'Y' 2 --> "Error: Invalid User Function" 'X*Y/(X^2+Y^2)' 'Y' 2 --> > >Why am I getting that message? > >If I delete 'SIMPLIFY' then get the correct result, obviously not >simplified: > >\<< \-> F V N > \<< F XQ 1 N > FOR K V DERIV > NEXT > \>> >\>> 'DERVN' STO > >'F(X,Y)=X*Y/(X^2+Y^2)' 'Y' 2 --> 'd2d2F(X,Y)=(SQ(X^2+Y^2)*(X*(2*Y)-(X* >(2*Y)+2*(X*Y)))-(X*(X^2+Y^2)-X*Y*(2*Y))*(2*((X^2+Y^2)*(2*Y))))/SQ(SQ >(X^2+Y^2))' > >then SIMPLIFY: 'd2d2F(X,Y)=-((6*Y*X^3-2*Y^3*X)/ >(X^6+3*Y^2*X^4+3*Y^4*X^2+Y^6))' > >Cheers, >Simone.
From: supergems on 15 Oct 2009 13:41 I don't understand why when I type an expression F (X, Y... )=... I get an error message, while applying DERVN (with SIMPLIFY, without SIMPLIFY no problem ) individually to members of that equation okay.
From: supergems on 15 Oct 2009 14:02
I solved the problem by moving SIMP after NEXT :-) : \<< \-> F V N \<< F XQ 1 N FOR K V DERIV NEXT \>> SIMPLIFY \>> 'STO' DERVN 'F(X,Y)=X*Y/(X^2+Y^2)' 'Y' 2 --> 'd2d2F(X,Y)=-((6*Y*X^3-2*Y^3*X)/ (X^6+3*Y^2*X^4+3*Y^4*X^2+Y^6))' |