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% Document Info
\author{pablocdch}
\pdfinfo{
  /Title (algebra-calculus-i-and-ii.pdf)
  /Creator (Cheatography)
  /Author (pablocdch)
  /Subject (Algebra, Calculus I \& II Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Algebra, Calculus I \& II Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{pablocdch} via \textcolor{DarkBackground}{\uline{cheatography.com/30131/cs/8927/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}pablocdch \\
  \uline{cheatography.com/pablocdch} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 9th January, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




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Expression & Derivative \tn 
% Row Count 1 (+ 1)
% Row 1
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f(x)=k & f'(x)=0 \tn 
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% Row 2
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% Row 3
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% Row 4
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f(x)=a\textasciicircum{}x\textasciicircum{} & f'(x)=a\textasciicircum{}x\textasciicircum{} lna \tn 
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% Row 5
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f(x)=kx & f'(x)=k \tn 
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% Row 6
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f(x)=1/x & f'(x)=-1/x\textasciicircum{}2\textasciicircum{} \tn 
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% Row 7
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f(x)=ln x & f'(x)=1/x \tn 
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% Row 8
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f(x)=e\textasciicircum{}u\textasciicircum{} & f'(x)=u'.e\textasciicircum{}u\textasciicircum{} \tn 
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% Row 9
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f(x)=logaX & f'(x)=1/x lna \tn 
% Row Count 10 (+ 1)
% Row 10
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f(x)=sen(x) & f'(x)=cos(x) \tn 
% Row Count 11 (+ 1)
% Row 11
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f(x)=sec(x) & f'(x)=sec(x).tan(x) \tn 
% Row Count 12 (+ 1)
% Row 12
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f(x)=arcsen(x) & f'(x)=1/√1-x\textasciicircum{}2\textasciicircum{} \tn 
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% Row 13
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f(x)=cos(x) & f'(x)=-sen(x) \tn 
% Row Count 14 (+ 1)
% Row 14
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f(x)=csc(x) & f'(x)=-csc(x).ctg(x) \tn 
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% Row 15
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f(x)=arccos(x) & f'(x)=-1/√1-x\textasciicircum{}2\textasciicircum{} \tn 
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% Row 16
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f(x)=tan(x) & f'(x)=sec\textasciicircum{}2\textasciicircum{}(x) \tn 
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% Row 17
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f(x)=ctg(x) & f'(x)=-csc\textasciicircum{}2\textasciicircum{}(x) \tn 
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% Row 18
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f(x)=arctan(x) & f'(x)=1/1+x\textasciicircum{}2\textasciicircum{} \tn 
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% Row 1
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% Row 2
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% Row 3
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% Row 4
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% Row 5
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% Row 6
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% Row 7
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% Row 8
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% Row 9
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% Row 11
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% Row 12
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% Row 13
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% Row 14
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% Row 15
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% Row 16
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% Row 3
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% Row 5
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\mymulticolumn{1}{x{5.377cm}}{Given x\textasciicircum{}2+ax+b=0, then you have to find two numbers that when {\bf{multiplied }}give you {\bf{B}} and {\bf{added}} give you {\bf{a}}.  \newline % Row Count 3 (+ 3)
{\bf{Example:}} \newline % Row Count 4 (+ 1)
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% Row 1
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% Row 0
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0/n & 0 \tn 
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% Row 1
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n/∞ & 0 \tn 
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% Row 2
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n/0 & ∞ \tn 
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% Row 0
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% Row 1
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logaA=lne & 1 \tn 
% Row Count 2 (+ 1)
% Row 2
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% Row 3
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loga(m.n) & logaM + logaN \tn 
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% Row 4
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loga(m/n) & logaM - logaM \tn 
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% Row 1
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a\textasciicircum{}1\textasciicircum{} & a \tn 
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% Row 2
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% Row Count 3 (+ 1)
% Row 3
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% Row Count 4 (+ 1)
% Row 4
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(a.b)\textasciicircum{}n\textasciicircum{} & a\textasciicircum{}n\textasciicircum{} . b\textasciicircum{}n\textasciicircum{} \tn 
% Row Count 5 (+ 1)
% Row 5
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(a/b)\textasciicircum{}n\textasciicircum{} & a\textasciicircum{}n\textasciicircum{}/b\textasciicircum{}n\textasciicircum{} \tn 
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% Row 6
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(a\textasciicircum{}m\textasciicircum{})\textasciicircum{}n\textasciicircum{} & a\textasciicircum{}m.n\textasciicircum{} \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
a\textasciicircum{}n/m\textasciicircum{} & raiz m de a\textasciicircum{}n\textasciicircum{} \tn 
% Row Count 8 (+ 1)
% Row 8
\SetRowColor{LightBackground}
a\textasciicircum{}-1\textasciicircum{} & 1/a \tn 
% Row Count 9 (+ 1)
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Trigonometrical identities}}  \tn
% Row 0
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% Row Count 1 (+ 1)
% Row 1
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% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{cosec$^{\textrm{2}}$ α = 1 + cotg$^{\textrm{2}}$ α} \tn 
% Row Count 3 (+ 1)
% Row 3
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% Row Count 4 (+ 1)
% Row 4
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% Row Count 5 (+ 1)
% Row 5
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% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
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% Row Count 7 (+ 1)
% Row 7
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\mymulticolumn{1}{x{5.377cm}}{cos(x + y) = cos(x) cos(y) − sin(x) sin(y)} \tn 
% Row Count 8 (+ 1)
% Row 8
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\mymulticolumn{1}{x{5.377cm}}{tan(x + y) = (tan(x) + tan(y))/(1 − tan(x) tan(y))} \tn 
% Row Count 10 (+ 2)
% Row 9
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\mymulticolumn{1}{x{5.377cm}}{sin(x − y) = sin(x) cos(y) − cos(x) sin(y)} \tn 
% Row Count 11 (+ 1)
% Row 10
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\mymulticolumn{1}{x{5.377cm}}{cos(x − y) = cos(x) cos(y) + sin(x) sin(y)} \tn 
% Row Count 12 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{tan(x − y) = (tan(x) − tan(y))/(1 + tan(x) tan(y))} \tn 
% Row Count 14 (+ 2)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{sin (2 x) = 2 sin (x) cos (x)} \tn 
% Row Count 15 (+ 1)
% Row 13
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cos (2 x) = cos2 (x) − sin2 (x)} \tn 
% Row Count 16 (+ 1)
% Row 14
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\mymulticolumn{1}{x{5.377cm}}{cos (2 x) = 2 cos2 (x) − 1} \tn 
% Row Count 17 (+ 1)
% Row 15
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{tan (2 x) = (2 tan (x))/(1 − tan2 (x))} \tn 
% Row Count 18 (+ 1)
% Row 16
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{sin2 (x) = 1/2 (1 − cos (2 x))} \tn 
% Row Count 19 (+ 1)
% Row 17
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cos2 (x) = 1/2 (1 + cos (2 x))} \tn 
% Row Count 20 (+ 1)
% Row 18
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{sin (x) cos (x) = 1/2 sin (2 x)} \tn 
% Row Count 21 (+ 1)
% Row 19
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{sin (x) sin (y) = 1/2 (cos (x − y) − cos (x + y))} \tn 
% Row Count 23 (+ 2)
% Row 20
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{sin (x) cos (y) = 1/2 (sin (x − y) + sin (x + y))} \tn 
% Row Count 25 (+ 2)
% Row 21
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cos (x) cos (y) = 1/2 (cos (x − y) + cos (x + y))} \tn 
% Row Count 27 (+ 2)
% Row 22
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{csc(x) = 1/sin(x)} \tn 
% Row Count 28 (+ 1)
% Row 23
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{sec(x) = 1/cos(x)} \tn 
% Row Count 29 (+ 1)
% Row 24
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{cot(x) = cos(x)/tan(x)} \tn 
% Row Count 30 (+ 1)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Trigonometrical identities (cont)}}  \tn
% Row 25
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{sin(−x) = − sin(x)} \tn 
% Row Count 1 (+ 1)
% Row 26
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cos(−x) = cos(x)} \tn 
% Row Count 2 (+ 1)
% Row 27
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{tan(−x) = − tan(x)} \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}