\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{Zulle} \pdfinfo{ /Title (calculo-i-regras-de-derivacao.pdf) /Creator (Cheatography) /Author (Zulle) /Subject (Calculo I - regras de derivação Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{7BE38C} \definecolor{LightBackground}{HTML}{EEFBF0} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Calculo I - regras de derivação Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Zulle} via \textcolor{DarkBackground}{\uline{cheatography.com/126577/cs/24538/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}Zulle \\ \uline{cheatography.com/zulle} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 29th September, 2020.\\ Updated 30th September, 2020.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Definição}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\} f´(x) = lim (f(x0+h) - f(x0))/h} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Df´(x) c Df(x)} \tn % Row Count 2 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Derivada em um ponto}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\} g´(x) = lim ( g(x) - g(x0) ) / (x - x0)} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{P = (x0,y0)} \tn % Row Count 2 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.53827 cm} x{2.43873 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Reta tangente à g(x) em um ponto P}} \tn % Row 0 \SetRowColor{LightBackground} 1. achar derivada de g(x) & g´(x) \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} 2. achar m & m = lim da derivada em P \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{3. substituir P na eq da reta tangente} \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.28482 cm} x{1.69218 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Reta Tangente}} \tn % Row 0 \SetRowColor{LightBackground} y - y0 = m ( x - x0 ) & P = (x0,y0) \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Reta Normal}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{y - y0 = (-1/m) ( x - x0 )} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.29402 cm} x{3.68298 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Regras de Derivação}} \tn % Row 0 \SetRowColor{LightBackground} k & 0 \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} x\textasciicircum{}n & n.x\textasciicircum{}n-1 \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} k.f(x) & k.f´(x) \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} f(x) +- g(x) & f´(x) +- g´(x) \tn % Row Count 5 (+ 2) % Row 4 \SetRowColor{LightBackground} f(x).g(x) & f´(x).g(x) + f(x)g´(x) \tn % Row Count 6 (+ 1) % Row 5 \SetRowColor{white} f(x)/g(x) & (f´(x).g(x) - f(x)g´(x))/(f(x))\textasciicircum{}2 \tn % Row Count 8 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.14011 cm} x{2.83689 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Log e exponecial}} \tn % Row 0 \SetRowColor{LightBackground} log a (x) & 1 / (ln a).x \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} a\textasciicircum{}x & a\textasciicircum{}x (ln a) \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} ln x & 1/x \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} e\textasciicircum{}x & e\textasciicircum{}x \tn % Row Count 4 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.59264 cm} x{3.38436 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Trigonométricas}} \tn % Row 0 \SetRowColor{LightBackground} sen(x) & cos(x) \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} cos(x) & - sen(x) \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} tg(x) & sec\textasciicircum{}2 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} cotg(x) & - cossec\textasciicircum{}2 \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} sec(x) & sec(x).tg(x) \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} cossec(x) & - cossec(x).cotg(x) \tn % Row Count 6 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.64241 cm} x{3.33459 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Trigonométricas Inversas}} \tn % Row 0 \SetRowColor{LightBackground} arcsen(x) & 1 / (1-x\textasciicircum{}2\textasciicircum{})\textasciicircum{}1/2\textasciicircum{} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} arccos(x) & -1 / (1-x\textasciicircum{}2\textasciicircum{})\textasciicircum{}1/2\textasciicircum{} \tn % Row Count 2 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.38896 cm} x{2.58804 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Trigonométricas Inversas}} \tn % Row 0 \SetRowColor{LightBackground} arctg(x) & 1 / 1+x\textasciicircum{}2\textasciicircum{} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} arccotg(x) & -1 / 1+x\textasciicircum{}2\textasciicircum{} \tn % Row Count 2 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Regra da Cadeia}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{1. para função composta} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{2. separe as funções externa e interna} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{3. derive externa e interna} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{fog(x) = f´(g(x)).g´(x)} \tn % Row Count 4 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{NOTAS}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/zulle_1601402129_trigonometry_basic-74.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Implícita}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{1. derive {\bf{x}} normalmente} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{2. derive {\bf{y}} como se fosse uma composta (cadeia)} \tn % Row Count 3 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{3. isole {\bf{y´}}} \tn % Row Count 4 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}