% (find-LATEX "2024-1-C3-diferencial-total.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2024-1-C3-diferencial-total.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2024-1-C3-diferencial-total.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2024-1-C3-diferencial-total.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2024-1-C3-diferencial-total.pdf"))
% (defun e () (interactive) (find-LATEX "2024-1-C3-diferencial-total.tex"))
% (defun o () (interactive) (find-LATEX "2024-1-C3-diferencial-total.tex"))
% (defun u () (interactive) (find-latex-upload-links "2024-1-C3-diferencial-total"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2024-1-C3-diferencial-total.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
%          (code-eec-LATEX "2024-1-C3-diferencial-total")
% (find-pdf-page   "~/LATEX/2024-1-C3-diferencial-total.pdf")
% (find-sh0 "cp -v  ~/LATEX/2024-1-C3-diferencial-total.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2024-1-C3-diferencial-total.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2024-1-C3-diferencial-total.pdf")
%   file:///home/edrx/LATEX/2024-1-C3-diferencial-total.pdf
%               file:///tmp/2024-1-C3-diferencial-total.pdf
%           file:///tmp/pen/2024-1-C3-diferencial-total.pdf
%  http://anggtwu.net/LATEX/2024-1-C3-diferencial-total.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-cps   "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-anggs "Caepro5 Piecewise2 Maxima2")
% (find-MM-aula-links "2024-1-C3-diferencial-total" "3" "c3m241dertotal" "c3dt")

% «.defs»		(to "defs")
% «.defs-T-and-B»	(to "defs-T-and-B")
% «.defs-caepro»	(to "defs-caepro")
% «.defs-pict2e»	(to "defs-pict2e")
% «.defs-maxima»	(to "defs-maxima")
% «.defs-V»		(to "defs-V")
% «.title»		(to "title")
% «.links»		(to "links")
% «.links-stewart»	(to "links-stewart")
% «.links-quadros»	(to "links-quadros")
% «.links-find-es»	(to "links-find-es")
% «.depends»		(to "depends")
% «.gradefs»		(to "gradefs")
% «.exercicios»		(to "exercicios")



\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
\usepackage{colorweb}                  % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
%\usepackage{proof}   % For derivation trees ("%:" lines)
%\input diagxy        % For 2D diagrams ("%D" lines)
%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21}               % (find-LATEX "edrx21.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%
\begin{document}

% «defs»  (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")

\def\drafturl{http://anggtwu.net/LATEX/2024-1-C3.pdf}
\def\drafturl{http://anggtwu.net/2024.1-C3.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}

% (find-LATEX "2024-1-C2-carro.tex" "defs-caepro")
% (find-LATEX "2024-1-C2-carro.tex" "defs-pict2e")

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

% «defs-T-and-B»  (to ".defs-T-and-B")
\long\def\ColorDarkOrange#1{{\color{orange!90!black}#1}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B       (#1 pts){\ColorDarkOrange{\bf(#1 pts)}}

% «defs-caepro»  (to ".defs-caepro")
%L dofile "Caepro5.lua"              -- (find-angg "LUA/Caepro5.lua" "LaTeX")
\def\Caurl   #1{\expr{Caurl("#1")}}
\def\Cahref#1#2{\href{\Caurl{#1}}{#2}}
\def\Ca      #1{\Cahref{#1}{#1}}

% «defs-pict2e»  (to ".defs-pict2e")
%L dofile "Piecewise2.lua"           -- (find-LATEX "Piecewise2.lua")
%L --dofile "Escadas1.lua"           -- (find-LATEX "Escadas1.lua")
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
\def\pictnaxesstyle{\color{GrayPale}\linethickness{0.5pt}}
\celllower=2.5pt

% «defs-maxima»  (to ".defs-maxima")
%L dofile "Maxima2.lua"              -- (find-angg "LUA/Maxima2.lua")
\pu

% «defs-V»  (to ".defs-V")
%L --- See: (find-angg "LUA/MiniV1.lua" "problem-with-V")
%L V = MiniV
%L v = V.fromab
\pu


%  _____ _ _   _                               
% |_   _(_) |_| | ___   _ __   __ _  __ _  ___ 
%   | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
%   | | | | |_| |  __/ | |_) | (_| | (_| |  __/
%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c3m241dertotalp 1 "title")
% (c3m241dertotala   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 3 - 2024.1}

\bsk

Aula 21: A diferencial total

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://anggtwu.net/2024.1-C3.html}

\end{center}

\newpage

% «links»  (to ".links")
% (c3m241dertotalp 2 "links")
% (c3m241dertotala   "links")
% (c2m241dip 2 "links")
% (c2m241dia   "links")

{\bf Links}

\scalebox{0.6}{\def\colwidth{14cm}\firstcol{

% «links-stewart»  (to ".links-stewart")
% (find-books "__analysis/__analysis.el" "stewart-pt" "791" "14 Derivadas Parciais")
% (find-books "__analysis/__analysis.el" "stewart-pt" "811" "14.3 Derivadas Parciais")
% (find-books "__analysis/__analysis.el" "stewart-pt" "823" "14.4 Planos Tangentes e Aproximações")
% (find-books "__analysis/__analysis.el" "stewart-pt" "827" "diferencial dz")
% (find-books "__analysis/__analysis.el" "stewart-pt" "827" "diferenciação total")
% (find-books "__analysis/__analysis.el" "stewart-pt" "831" "14.5 A Regra da Cadeia")
\par \Ca{StewPtCap14p5} (p.791) 14 Derivadas Parciais
\par \Ca{StewPtCap14p25} (p.811) 14.3 Derivadas Parciais
\par \Ca{StewPtCap14p37} (p.823) 14.4 Planos Tangentes e Aproximações
\par \Ca{StewPtCap14p41} (p.827) a diferencial dz ... diferenciação total
\par \Ca{StewPtCap14p45} (p.831) 14.5 A regra da cadeia

\msk

% «links-quadros»  (to ".links-quadros")
% (find-angg ".emacs" "c3q241" "45" "jul29: a diferencial total")
\par \Ca{3iQ45} Quadros da aula de 29/jul/2024

\msk

% «links-find-es»  (to ".links-find-es")
% (find-es "maxima" "2024.1-depends")
% (find-es "maxima" "2024.1-gradefs")
{\footnotesize
\par \url{http://anggtwu.net/e/maxima.e.html\#2024.1-depends}
\par \url{http://anggtwu.net/e/maxima.e.html\#2024.1-gradefs}

}
\par \texttt{(find-es "maxima" "2024.1-depends")}
\par \texttt{(find-es "maxima" "2024.1-gradefs")}


}\anothercol{
}}

\newpage

%  ____                            _     
% |  _ \  ___ _ __   ___ _ __   __| |___ 
% | | | |/ _ \ '_ \ / _ \ '_ \ / _` / __|
% | |_| |  __/ |_) |  __/ | | | (_| \__ \
% |____/ \___| .__/ \___|_| |_|\__,_|___/
%            |_|                         
%
% «depends»  (to ".depends")
% (c3m241dertotalp 3 "depends")
% (c3m241dertotala   "depends")

{\bf Depends}

%M (%i1) y : x^2;
%M (%o1) x^2
%M (%i2) z : sin(y);
%M (%o2) \sin x^2
%M (%i3) diff(z, x);
%M (%o3) 2\,x\,\cos x^2
%M (%i4) diff(z, x, 2);
%M (%o4) 2\,\cos x^2-4\,x^2\,\sin x^2
%M (%i5) values;
%M (%o5) \left[ y , z \right] 
%M (%i6) 
%M remvalue(all);
%M (%o6) \left[ y , z \right] 
%M (%i7) values;
%M (%o7) \left[  \right] 
%L maximahead:sa("depends", "")
\pu

%M (%i8) diff(y, x);
%M (%o8) 0
%M (%i9) depends(y, x);
%M (%o9) \left[ y\left(x\right) \right] 
%M (%i10) depends(z, y);
%M (%o10) \left[ z\left(y\right) \right] 
%M (%i11) dependencies;
%M (%o11) \left[ y\left(x\right) , z\left(y\right) \right] 
%M (%i12) diff(y, x);
%M (%o12) {\frac{d}{d\,x}}\,y
%M (%i13) diff(z, x);
%M (%o13) {\frac{d}{d\,x}}\,y\,\left({\frac{d}{d\,y}}\,z\right)
%M (%i14) diff(z, x, 2);
%M (%o14) \left({\frac{d}{d\,x}}\,y\right)^2\,\left({\frac{d^2}{d\,y^2}}\,z\right)+{\frac{d^2}{d\,x^2}}\,y\,\left({\frac{d}{d\,y}}\,z\right)
%L maximahead:sa("depends 2", "")
\pu

%M (%i15) o1 : diff(z, x);
%M (%o15) {\frac{d}{d\,x}}\,y\,\left({\frac{d}{d\,y}}\,z\right)
%M (%i16) o2 : diff(z, x, 2);
%M (%o16) \left({\frac{d}{d\,x}}\,y\right)^2\,\left({\frac{d^2}{d\,y^2}}\,z\right)+{\frac{d^2}{d\,x^2}}\,y\,\left({\frac{d}{d\,y}}\,z\right)
%M (%i17) o3 : at(o1, [z=sin(y), y=x^2]);
%M (%o17) {\frac{d}{d\,x}}\,x^2\,\left(\left.{\frac{d}{d\,y}}\,\sin y\right|_{y=x^2}\right)
%M (%i18) o4 : at(o2, [z=sin(y), y=x^2]);
%M (%o18) \left({\frac{d}{d\,x}}\,x^2\right)^2\,\left(\left.{\frac{d^2}{d\,y^2}}\,\sin y\right|_{y=x^2}\right)+{\frac{d^2}{d\,x^2}}\,x^2\,\left(\left.{\frac{d}{d\,y}}\,\sin y\right|_{y=x^2}\right)
%M (%i19) o5 : ev(o3, 'derivative, 'at);
%M (%o19) 2\,x\,\cos x^2
%M (%i20) o6 : ev(o4, 'derivative, 'at);
%M (%o20) 2\,\cos x^2-4\,x^2\,\sin x^2
%M (%i21) 
%L maximahead:sa("depends 3", "")
\pu


\scalebox{0.4}{\def\colwidth{6cm}\firstcol{

\vspace*{0cm}

\def\hboxthreewidth {8cm}
\ga{depends}

}\def\colwidth{9cm}\anothercol{

\vspace*{0cm}

\def\hboxthreewidth {11cm}
\ga{depends 2}

}\def\colwidth{6cm}\anothercol{

\vspace*{0cm}

\def\hboxthreewidth {14cm}
\ga{depends 3}

}}



\newpage

%   ____               _       __     
%  / ___|_ __ __ _  __| | ___ / _|___ 
% | |  _| '__/ _` |/ _` |/ _ \ |_/ __|
% | |_| | | | (_| | (_| |  __/  _\__ \
%  \____|_|  \__,_|\__,_|\___|_| |___/
%                                     
% «gradefs»  (to ".gradefs")
% (c3m241dertotalp 4 "gradefs")
% (c3m241dertotala   "gradefs")
% (find-es "maxima" "2024.1-gradefs")

{\bf Gradefs}


%M (%i1) diff  (sin(x), x);
%M (%o1) \cos x
%M (%i2) gradef(sin(x), sqrt(1-sin(x)^2));
%M (%o2) \sin x
%M (%i3) diff  (sin(x), x);
%M (%o3) \sqrt{1-\left(\sin x\right)^2}
%M (%i4)  texput(y_x,  "y_x")$
%M (%i5)  texput(z_y,  "z_y")$
%M (%i6)  texput(y_xx, "y_{xx}")$
%M (%i7)  texput(z_yy, "z_{yy}")$
%M (%i8)  gradef(y,x,   y_x)$
%M (%i9)  gradef(z,y,   z_y)$
%M (%i10) gradef(y_x,x, y_xx)$
%M (%i11) gradef(z_y,y, z_yy)$
%L maximahead:sa("gradefs", "")
\pu

%M (%i12) diff(y, x);
%M (%o12) y_x
%M (%i13) diff(z, x);
%M (%o13) y_x\,z_y
%M (%i14) diff(z, x, 2);
%M (%o14) y_x^2\,z_{yy}+y_{xx}\,z_y
%M (%i15) o1 : diff(y);
%M (%o15) y_x\,dx
%M (%i16) o2 : diff(z);
%M (%o16) z_y\,dy
%M (%i17) o3 : subst([del(y)=diff(y)], o2);
%M (%o17) y_x\,z_y\,dx
%M (%i18) 
%L maximahead:sa("gradefs 2", "")
\pu

\scalebox{0.5}{\def\colwidth{9cm}\firstcol{

\vspace*{0cm}
\def\hboxthreewidth {10cm}
\ga{gradefs}

}\anothercol{

\vspace*{0cm}
\def\hboxthreewidth {12cm}
\ga{gradefs 2}

}}



\newpage

%  _____                   _      _           
% | ____|_  _____ _ __ ___(_) ___(_) ___  ___ 
% |  _| \ \/ / _ \ '__/ __| |/ __| |/ _ \/ __|
% | |___ >  <  __/ | | (__| | (__| | (_) \__ \
% |_____/_/\_\___|_|  \___|_|\___|_|\___/|___/
%                                             
% «exercicios»  (to ".exercicios")
% (c3m241dertotalp 5 "exercicios")
% (c3m241dertotala   "exercicios")



\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}



% Local Variables:
% coding: utf-8-unix
% ee-tla: "c3dt"
% ee-tla: "c3m241dertotal"
% End: