%% Created by Maple 15.00, Windows 7
%% Source Worksheet: p57.mw
%% Generated: Tue May 08 16:58:50 CST 2012
\documentclass{article}
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\mapleinline{inert}{2d}{f1 := z = f(x+y, z+y)}{\[\displaystyle {\it f1}\, := \,z=f \left( x+y,z+y \right) \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{z = f(x+y, z+y)}{\[\displaystyle z=f \left( x+y,z+y \right) \]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{implicitdiff(f1, z, x, x)}{\[\displaystyle {\it implicitdiff} \left( {\it f1},z,x,x \right) \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)^2-2*(D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)^2)/(-1-3*(D[2](f))(x+y, z+y)^2+3*(D[2](f))(x+y, z+y)+(D[2](f))(x+y, z+y)^3)}{\[\displaystyle -{\frac { \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}-2\, \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{2}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}}{-1-3\, \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}\\
\mbox{}+3\,D_{{2}} \left( f \right)  \left( x+y,z+y \right) + \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{3}}}\]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{implicitdiff(f1, z, x, y)}{$\displaystyle {\it implicitdiff} \left( {\it f1},z,x,y \right) $}
\mapleinline{inert}{2d}{}{$\displaystyle $}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)^2-2*(D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)-(D[1, 2](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 2](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)^2+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y))/(-1-3*(D[2](f))(x+y, z+y)^2+3*(D[2](f))(x+y, z+y)+(D[2](f))(x+y, z+y)^3)}{\[\displaystyle -{\frac { \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}-2\, \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{2}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}- \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{2}} \left( f \right)  \left( x+y,z+y \right) + \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}}{-1-3\, \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}+3\,D_{{2}} \left( f \right)  \left( x+y,z+y \right) + \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{3}}}\]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{implicitdiff(f1, z, y, y)}{\[\displaystyle {\it implicitdiff} \left( {\it f1},z,y,y \right) \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)^2-2*(D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)^2+2*(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y))/(-1-3*(D[2](f))(x+y, z+y)^2+3*(D[2](f))(x+y, z+y)+(D[2](f))(x+y, z+y)^3)}{\[\displaystyle -{\frac { \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}-2\, \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{2}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}-2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{2}} \left( f \right)  \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}+2\, \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y \right) D_{{1}} \left( f \right)  \left( x+y,z+y \right) \\
\mbox{}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y \right) }{-1-3\, \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{2}+3\,D_{{2}} \left( f \right)  \left( x+y,z+y \right) + \left( D_{{2}} \left( f \right)  \left( x+y,z+y \right)  \right) ^{3}\\
\mbox{}}}\]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{f2 := f(x+y, z+y, z+x) = 0}{\[\displaystyle {\it f2}\, := \,f \left( x+y,z+y,z+x \right) =0\]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{f(x+y, z+y, z+x) = 0}{\[\displaystyle f \left( x+y,z+y,z+x \right) =0\]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{dx2 := simplify(implicitdiff(f2, z, x, x))}{\[\displaystyle {\it dx2}\, := \,{\it simplify} \left( {\it implicitdiff} \left( {\it f2},z,x,x \right) \\
\mbox{} \right) \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{-(2*(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)+(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[1, 1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2)/(3*(D[2](f))(x+y, z+y, z+x)^2*(D[3](f))(x+y, z+y, z+x)+3*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2](f))(x+y, z+y, z+x)^3+(D[3](f))(x+y, z+y, z+x)^3)}{\[\displaystyle -{\frac {2\, \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}-2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +2\, \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}+2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}-2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}+ \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}}{3\, \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +3\,D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{3}+ \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{3}}}\]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\begin{Maple Normal}{
\begin{Maple Normal}{
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
}\end{Maple Normal}
}\end{Maple Normal}
\mapleinline{inert}{2d}{simplify(implicitdiff(f2, z, x, y))}{\[\displaystyle {\it simplify} \left( {\it implicitdiff} \left( {\it f2},z,x,y\\
\mbox{} \right)  \right) \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[1, 1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2-(D[2, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2-(D[3, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+2*(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x))/(3*(D[2](f))(x+y, z+y, z+x)^2*(D[3](f))(x+y, z+y, z+x)+3*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2](f))(x+y, z+y, z+x)^3+(D[3](f))(x+y, z+y, z+x)^3)}{\[\displaystyle -{\frac { \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}- \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}- \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+2\, \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}-2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) }{3\, \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}+3\,D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}+ \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{3}\\
\mbox{}+ \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{3}}}\]}
\end{maplelatex}
\end{maplegroup}
\begin{Maple Normal}{
\begin{Maple Normal}{
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
}\end{Maple Normal}
}\end{Maple Normal}
\mapleinline{inert}{2d}{simplify(implicitdiff(f2, z, y, y))}{\[\displaystyle {\it simplify} \left( {\it implicitdiff} \left( {\it f2},z,y,y \right) \\
\mbox{} \right) \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{-(2*(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[1, 2](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)+(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[1, 1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[1, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2)/(3*(D[2](f))(x+y, z+y, z+x)^2*(D[3](f))(x+y, z+y, z+x)+3*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2](f))(x+y, z+y, z+x)^3+(D[3](f))(x+y, z+y, z+x)^3)}{\[\displaystyle -{\frac {2\, \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}-2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}-2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +2\, \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right) \\
\mbox{}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}+ \left( D_{{1,1}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+2\, \left( D_{{1,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}-2\, \left( D_{{1,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}+ \left( D_{{2,2}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+2\, \left( D_{{2,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{1}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}+ \left( D_{{3,3}} \right)  \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}}{3\, \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right) +3\,D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{2}\\
\mbox{}+ \left( D_{{2}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{3}+ \left( D_{{3}} \left( f \right)  \left( x+y,z+y,z+x \right)  \right) ^{3}}}\]}
\end{maplelatex}
\end{maplegroup}
\begin{Maple Normal}{
\begin{Maple Normal}{
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
}\end{Maple Normal}
}\end{Maple Normal}
\end{CJK}
\end{document}