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% 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{
}}
}
% Local Variables:
% coding: utf-8-unix
% ee-tla: "c26d"
% ee-tla: "c2m251example6d"
% End: