% This file:
%   http://anggtwu.net/LATEX/2025-1-C2-example-6-defs.tex.html
%   http://anggtwu.net/LATEX/2025-1-C2-example-6-defs.tex
%          (find-angg "LATEX/2025-1-C2-example-6-defs.tex")
% Author: Eduardo Ochs <eduardoochs@gmail.com>
%
% (defun e () (interactive) (find-angg "LATEX/2025-1-C2-example-6-defs.tex"))
% (defun o () (interactive) (find-LATEX "2025-1-C2-S-defs.tex"))


% «.und»		(to "und")
% «.body»		(to "body")
% «.highlight»		(to "highlight")
% «.example-6-with»	(to "example-6-with")
% «.example-6-just-5»	(to "example-6-just-5")
% «.example-6-just-6»	(to "example-6-just-6")
% «.example-6-just-7»	(to "example-6-just-7")
% «.example-6-just-9»	(to "example-6-just-9")
% «.example-6-just-10»	(to "example-6-just-10")
% «.HH»			(to "HH")


% (c2m251justp 2 "links-stewart")
% (c2m251justa   "links-stewart")
% (c2m251justp 4 "example-6")
% (c2m251justa   "example-6")
% (c2m251sda "TFC2")
% (c2m251sda "TFC2" "(RDC)")
% (c2m251sda "TFC2" "(RMC)")
% (c2m251sda "TFC2" "(RPot)")
% (c2m251sda "TFC2" "(RSoma)")
% (c2m251sda "TFC2" "(RProd)")
% (c2m251sda "TFC2" "(RC)")
\input 2025-1-C2-S-defs.tex   % (find-LATEX "2025-1-C2-S-defs.tex")

\sa{(RProd v)}{\pmat{
  \ddx(f(x)g(x))
  \;=\; \ph{mmm} \\
  f(x) \ddx g(x) + g(x) \ddx f(x)
  }}

% «und»  (to ".und")
\def\und    #1#2{\underbrace{#1}_{\textstyle #2}}
\def\undph#1#2#3{\underbrace{\phantom{#1}#2\phantom{#1}}_{\textstyle #3}}

% «body»  (to ".body")
% (c2m251example6tp 2 "body")
% (c2m251example6tp 2 "body")
% (c2m251example6da   "body")
% (sbcp 4 "example-6-defs")
% (sbca   "example-6-defs")
% (c2m251justp 4 "example-6")
% (c2m251justa   "example-6")
% (c2m251sda "eq-if")
% (c2m251sda "eq-p")

\def\veja#1{\text{Veja \Ca{#1}}}
\def\porcom#1#2{\text{Por \ga{#1} com $#2$}}
\def\Por#1{\text{Por }#1}
\def\Por#1{\text{Por }\setdepthto{0pt}{#1}}



\sa{Example 6: body}{
  F(x)  &\ga{=}{1}& (6x^3)(7x^4) \\
  \ga{p}{2L}{F'(x)}
        &\ga{=}{2}& \ga{p}{2R}{(\ga{p}{3L}{F(x)})'}                             \\
        &\ga{=}{3}& \ga{p}{4L}{(\ga{p}{3R}{(6x^3)(7x^4)})'}                     \\
        &\ga{=}{4}& \ga{p}{4}{\ddx((6x^3)(7x^4))}                               \\
        &\ga{=}{5}& \ga{p}{5R}{(6x^3)\ddx(7x^4) + (7x^4)\ga{p}{6L}{\ddx(6x^3)}} & \ga{just 5} \\
        &\ga{=}{6}& (6x^3)\ddx(7x^4) + (7x^4)·\ga{p}{6R}{6\ga{p}{7L}{\ddx x^3}} & \ga{just 6} \\
        &\ga{=}{7}& (6x^3)\ddx(7x^4) + (7x^4)·\ga{p}{8L}{6·\ga{p}{7R}{3 x^2}}   & \ga{just 7} \\
        &\ga{=}{8}& (6x^3)\ga{p}{9L}{\ddx(7x^4)} + (7x^4)\ga{p}{8R}{(18x^2)}    \\
        &\ga{=}{9}& (6x^3)·\ga{p}{9R}{7\ga{p}{10L}{\ddx x^4}} + (7x^4)(18x^2)   & \ga{just 9} \\
        &\ga{=}{10}& (6x^3)·\ga{p}{11L}{7·\ga{p}{10R}{4x^3}} + (7x^4)(18x^2)    & \ga{just 10} \\
        &\ga{=}{11}& (6x^3)\ga{p}{11R}{(28x^3)} + \ga{p}{12L}{(7x^4)(18x^2)}    \\
        &\ga{=}{12}& \ga{p}{13L}{(6x^3)(28x^3)} + \ga{p}{12R}{126x^6}           \\
        &\ga{=}{13}& \ga{p}{14L}{\ga{p}{13R}{168x^6} + 126x^6}                  \\
        &\ga{=}{14}& \ga{p}{14R}{294x^6}                                        \\
  }

\sa{Example 6}{
  \begin{array}{rcll}
  \ga{Example 6: body}
  \end{array}
  }

% «highlight»  (to ".highlight")
% (c2m251example6da    "Highlight")
% (c2m251sda "eq-if")
% (c2m251sda "eq-p")
\def\He#1{\sa{=.#1.}{foo}}   % highlight an `='
\def\Hp#1{\sa{p.#1.}{foo}}   % highlight a `p'
\sa{Highlight all ps}{\sa{p  after 2}{\standout{$\ga{2}$}_{\ga{1}}}}
\sa{Number    all =s}{\sa{eq after 1}{=_{\ga{1}}}}

\sa{Example 6 with all `='s and `p's}{
  \scalebox{0.6}{\def\colwidth{7cm}\firstcol{
      \vspace*{-1cm}
      $$\ga{Number all =s}
        \ga{Highlight all ps}
        \ga{Example 6}
      $$
    }\anothercol{
    }
  }}

\sa{Highlight  2}{\Hp {2L}\He {2} \Hp{2R}}
\sa{Highlight  3}{\Hp {3L}\He {3} \Hp{3R}}
\sa{Highlight  4}{\Hp {4L}\He {4} \Hp{4} }
\sa{Highlight  5}{\Hp {4} \He {5} \Hp{5R}   \sa{just  5}{\ga{Just 5 full}}}
\sa{Highlight  6}{\Hp {6L}\He {6} \Hp{6R}   \sa{just  6}{RMC}}
\sa{Highlight  7}{\Hp {7L}\He {7} \Hp{7R}   \sa{just  7}{RPowx}}
\sa{Highlight  8}{\Hp {8L}\He {8} \Hp{8R}}
\sa{Highlight  9}{\Hp {9L}\He {9} \Hp{9R}   \sa{just  9}{RMC}}
\sa{Highlight 10}{\Hp{10L}\He{10}\Hp{10R}   \sa{just 10}{RPowx}}
\sa{Highlight 11}{\Hp{11L}\He{11}\Hp{11R}}
\sa{Highlight 12}{\Hp{12L}\He{12}\Hp{12R}}
\sa{Highlight 13}{\Hp{13L}\He{13}\Hp{13R}}
\sa{Highlight 14}{\Hp{14L}\He{14}\Hp{14R}}




\newpage

% «example-6-with»  (to ".example-6-with")
% (sbcp 7 "example-6-with")
% (sbca   "example-6-with")

\Sa{Example 6 with}#1{\sa{1}{#1}\ga{Example 6 with after 1}}
\Sa{Example 6 with after 1}{
    \newpage
    \scalebox{0.7}{\def\colwidth{7cm}\firstcol{
      \vspace*{-1cm}
      \ga{1}
      $$\ga{Example 6}$$
    }\anothercol{
  }}}

\newpage

% «example-6-just-5»  (to ".example-6-just-5")
% (sbcp 5 "example-6-just-5")
% (sbca   "example-6-just-5")

\sa{Just 5 [RProd].1}   {\ga{[RProd]}}
\sa{Just 5 [RProd].2}   {\ga{(RProd v)}}
\sa{Just 5 [RProd]}     {\undph{mmmmm}
                               {\ga{Just 5 [RProd].1}}
                               {\ga{Just 5 [RProd].2}}}
\sa{Just 5 [S]}         {\bmat{f(x):= 6x^3 \\ g(x):=7x^4}}
\sa{Just 5 [RProd][S].1}{\ga{Just 5 [RProd]}
                         \ga{Just 5 [S]}}
\sa{Just 5 [RProd][S].2}{\pmat{\ddx((6x^3)(7x^4))
                               \;=\; \ph{mmm} \\
                               (6x^3) \ddx (7x^4) + (7x^4) \ddx (6x^3)}}
\sa{Just 5 [RProd][S]}  {\und{\ga{Just 5 [RProd][S].1}}
                             {\ga{Just 5 [RProd][S].2}}}
\sa{Just 5 short}       {\Por{\ga{Just 5 [RProd].1}}}
\sa{Just 5 full}        {\Por{\ga{Just 5 [RProd][S]}}}

% «example-6-just-6»  (to ".example-6-just-6")
% (sbcp 6 "example-6-just-6")
% (sbca   "example-6-just-6")

\sa{Just 6 [RMC].1}   {\ga{[RMC]}}
\sa{Just 6 [RMC].2}   {\ga{(RMC)}}
\sa{Just 6 [RMC]}     {\undph{mmmm}
                             {\ga{Just 6 [RMC].1}}
                             {\ga{Just 6 [RMC].2}}}
\sa{Just 6 [S]}       {\bmat{c:=6 \\ f(x):= x^3}}
\sa{Just 6 [RMC][S].1}{\ga{Just 6 [RMC]}
                       \ga{Just 6 [S]}}
\sa{Just 6 [RMC][S].2}{\pmat{\ddx(6x^3) \;=\; 6\ddx x^3}}
\sa{Just 6 [RMC][S]}  {\und{\ga{Just 6 [RMC][S].1}}
                           {\ga{Just 6 [RMC][S].2}}}
\sa{Just 6 short}     {\Por{\ga{Just 6 [RMC].1}}}
\sa{Just 6 full}      {\Por{\ga{Just 6 [RMC][S]}}}

% «example-6-just-7»  (to ".example-6-just-7")
% (sbcp 7 "example-6-just-7")
% (sbca   "example-6-just-7")

\sa{Just 7 [RPot].1}   {\ga{[RPot]}}
\sa{Just 7 [RPot].2}   {\ga{(RPot)}}
\sa{Just 7 [RPot]}     {\undph{mmmm}{\ga{Just 7 [RPot].1}}
                                    {\ga{Just 7 [RPot].2}}}
\sa{Just 7 [S]}        {\bmat{n:=3}}
\sa{Just 7 [RPot][S].1}{\ga{Just 7 [RPot]}
                        \ga{Just 7 [S]}}
\sa{Just 7 [RPot][S].2}{\pmat{\ddx x^3 \;=\; nx^{3-1}}}
\sa{Just 7 [RPot][S]}  {\und{\ga{Just 7 [RPot][S].1}}
                            {\ga{Just 7 [RPot][S].2}}}
\sa{Just 7 short}      {\Por{\ga{Just 7 [RPot].1}}}
\sa{Just 7 full}       {\Por{\ga{Just 7 [RPot][S]}}}

% «example-6-just-9»  (to ".example-6-just-9")
% (sbcp 8 "example-6-just-9")
% (sbca   "example-6-just-9")

\sa{Just 9 [RMC].1}   {\ga{[RMC]}}
\sa{Just 9 [RMC].2}   {\ga{(RMC)}}
\sa{Just 9 [RMC]}     {\undph{mmmm}{\ga{Just 9 [RMC].1}}
                                   {\ga{Just 9 [RMC].2}}}
\sa{Just 9 [S]}       {\bmat{c:=7 \\ f(x):= x^4}}
\sa{Just 9 [RMC][S].1}{\ga{Just 9 [RMC]}
                       \ga{Just 9 [S]}}
\sa{Just 9 [RMC][S].2}{\PBig{\ddx(7x^4) \;=\; 7\ddx x^4}}
\sa{Just 9 [RMC][S]}  {\und{\ga{Just 9 [RMC][S].1}}
                           {\ga{Just 9 [RMC][S].2}}}
\sa{Just 9 short}     {\Por{\ga{Just 9 [RMC].1}}}
\sa{Just 9 full}      {\Por{\ga{Just 9 [RMC][S]}}}

% «example-6-just-10»  (to ".example-6-just-10")
% (sbcp 9 "example-6-just-10")
% (sbca   "example-6-just-10")

\sa{Just 10 [RPot].1}   {\ga{[RPot]}}
\sa{Just 10 [RPot].2}   {\ga{(RPot)}}
\sa{Just 10 [RPot]}     {\undph{mmm}{\ga{Just 10 [RPot].1}}
                                    {\ga{Just 10 [RPot].2}}}
\sa{Just 10 [S]}        {\bmat{n:=4}}
\sa{Just 10 [RPot][S].1}{\ga{Just 10 [RPot]}
                         \ga{Just 10 [S]}}
\sa{Just 10 [RPot][S].2}{\PBig{\ddx x^4 \;=\; nx^{4-1}}}
\sa{Just 10 [RPot][S]}  {\und{\ga{Just 10 [RPot][S].1}}
                             {\ga{Just 10 [RPot][S].2}}}
\sa{Just 10 short}      {\Por{\ga{Just 10 [RPot][S]}}}
\sa{Just 10 full}       {\Por{\ga{Just 10 [RPot][S]}}}


% «HH»  (to ".HH")
% (c2m251example6tp 3 "HH")
% (c2m251example6ta   "HH")
% (c2m251example6da   "HH")

\def\HH#1{
  \newpage
  \scalebox{0.7}{\def\colwidth{7cm}\firstcol{
  \vspace*{-1cm}
  \ga{Highlight #1}
  $$\ga{Example 6}$$
}\anothercol{
}}
}





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% coding: utf-8-unix
% ee-tla: "c26d"
% ee-tla: "c2m251example6d"
% End:
