+\PassOptionsToPackage{unicode=true}{hyperref} % options for packages loaded elsewhere
+\PassOptionsToPackage{hyphens}{url}
+%
+\documentclass[twocolumn]{article}
+\usepackage{array}
+\usepackage{lmodern}
+\usepackage{amssymb,amsmath}
+\usepackage{ifxetex,ifluatex}
+\usepackage{multicol}
+\usepackage{fixltx2e} % provides \textsubscript
+\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
+ \usepackage[T1]{fontenc}
+ \usepackage[utf8]{inputenc}
+ \usepackage{textcomp} % provides euro and other symbols
+\else % if luatex or xelatex
+ \usepackage{unicode-math}
+ \defaultfontfeatures{Ligatures=TeX,Scale=MatchLowercase}
+\fi
+% use upquote if available, for straight quotes in verbatim environments
+\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
+% use microtype if available
+\IfFileExists{microtype.sty}{%
+\usepackage[]{microtype}
+\UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
+}{}
+\IfFileExists{parskip.sty}{%
+\usepackage{parskip}
+}{% else
+\setlength{\parindent}{0pt}
+\setlength{\parskip}{6pt plus 2pt minus 1pt}
+}
+\usepackage{hyperref}
+\hypersetup{
+ pdfauthor={Andrew Lorimer},
+ pdfborder={0 0 0},
+ breaklinks=true}
+\urlstyle{same} % don't use monospace font for urls
+\usepackage[margin=2cm]{geometry}
+\usepackage{supertabular, booktabs}
+% Fix footnotes in tables (requires footnote package)
+\IfFileExists{footnote.sty}{\usepackage{footnote}\makesavenoteenv{supertabular}}{}
+\usepackage{graphicx,grffile}
+\makeatletter
+\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
+\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi}
+\makeatother
+% Scale images if necessary, so that they will not overflow the page
+% margins by default, and it is still possible to overwrite the defaults
+% using explicit options in \includegraphics[width, height, ...]{}
+\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
+\setlength{\emergencystretch}{3em} % prevent overfull lines
+\providecommand{\tightlist}{%
+ \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
+\setcounter{secnumdepth}{0}
+% Redefines (sub)paragraphs to behave more like sections
+\ifx\paragraph\undefined\else
+\let\oldparagraph\paragraph
+\renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}}
+\fi
+\ifx\subparagraph\undefined\else
+\let\oldsubparagraph\subparagraph
+\renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}}
+\fi
+
+% set default figure placement to htbp
+\makeatletter
+\def\fps@figure{htbp}
+\makeatother
+
+\usepackage{supertabular}
+
+\author{Andrew Lorimer}
+\date{}
+
+\pagenumbering{gobble}
+
+\begin{document}
+% \begin{multicols}{2}
+\renewcommand{\arraystretch}{1.5}
+
+\hypertarget{spec---calculus}{%
+\section{Spec - Calculus}\label{spec---calculus}}
+
+\hypertarget{gradients}{%
+\subsection{Gradients}\label{gradients}}
+
+\[m \operatorname{of} x \in [a,b] = {{f(b)-f(a)}\over {b - a}} = {dy \over dx}\]
+
+\hypertarget{limit-theorems}{%
+\subsection{Limit theorems}\label{limit-theorems}}
+
+\begin{enumerate}
+\def\labelenumi{\arabic{enumi}.}
+\tightlist
+\item
+ For constant function \(f(x)=k\), \(\lim_{x \rightarrow a} f(x) = k\)
+\item
+ \(\lim_{x \rightarrow a} (f(x) \pm g(x)) = F \pm G\)
+\item
+ \(\lim_{x \rightarrow a} (f(x) \times g(x)) = F \times G\)
+\item
+ \({\lim_{x \rightarrow a} {f(x) \over g(x)}} = {F \over G}, G \ne 0\)
+\end{enumerate}
+
+\hypertarget{first-principles-derivative}{%
+\subsection{First principles
+derivative}\label{first-principles-derivative}}
+
+\[f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}\]
+
+\hypertarget{tangents-gradients}{%
+\subsection{Tangents \& gradients}\label{tangents-gradients}}
+
+\textbf{Tangent line} - defined by \(y=mx+c\) where
+\(m={dy \over dx}\)\\
+\textbf{Normal line} - \(\perp\) tangent
+(\(m_{\operatorname{tan}} \cdot m_{\operatorname{norm}} = -1\))\\
+\textbf{Secant} \(={{f(x+h)-f(x)} \over h}\)
+
+\hypertarget{derivatives}{%
+\subsection{Derivatives}\label{derivatives}}
+
+\tablehead{\hline \(f(x)\) & \(f^\prime(x)\) \\ \hline \\}
+\begin{supertabular}[]{@{}ll@{}}
+
+\(kx^n\) & \(knx^{n-1}\)\tabularnewline
+\(g(x) \pm h(x)\) & \(g^\prime (x) \pm h^\prime (x)\)\tabularnewline
+\(c\) & \(0\)\tabularnewline
+\({u \over v}\) &
+\({{(v{du \over dx} - u{dv \over dx}}) \div v^2}\)\tabularnewline
+\(uv\) & \(u{dv \over dx} + v{du \over dx}\)\tabularnewline
+\(f \circ g\) & \({dy \over du} \cdot {du \over dx}\)\tabularnewline
+\(\sin ax\) & \(a\cos ax\)\tabularnewline
+\(\sin(f(x))\) & \(f^\prime(x) \cdot \cos(f(x))\)\tabularnewline
+\(\cos ax\) & \(-a \sin ax\)\tabularnewline
+\(\cos(f(x))\) & \(f^\prime(x)(-\sin(f(x)))\) \\
+\(e^{ax}\) & \(ae^{ax}\)\tabularnewline
+\(\log_e {ax}\) & \(1 \over x\)\tabularnewline
+\(\log_e f(x)\) & \(f^\prime (x) \over f(x)\)\tabularnewline
+
+\end{supertabular}
+
+\hypertarget{product-rule-for-yuv}{%
+\subsection{\texorpdfstring{Product rule for
+\(y=uv\)}{Product rule for y=uv}}\label{product-rule-for-yuv}}
+
+\[{dy \over dx} = u{dv \over dx} + v{du \over dx}\]
+
+\subsection{Chain rule for $(f\circ g)$}
+
+$${dy \over dx} = {dy \over du} \cdot {du \over dx}$$
+
+% Function notation:
+
+$${\displaystyle (f\circ g)'=(f'\circ g)\cdot g'}=f'(g(x)) \cdot g'(x)$$
+
+% $$(f\circ g)^\prime(x)=f^\prime(g(x))g^\prime(x),\quad \text{where}\hspace{0.3em} (f\circ g)(x)=f(g(x))$$}
+
+\hypertarget{logarithms}{%
+\subsection{Logarithms}\label{logarithms}}
+
+\[\log_b (x) = n \quad \operatorname{where} \hspace{0.5em} b^n=x\]
+
+\subsubsection{Logarithmic identities}
+$\log_b (xy)=\log_b x + \log_b y$ \\
+$\log_b x^n = n \log_b x$ \\
+$\log_b y^{x^n} = x^n \log_b y$
+
+\hypertarget{integration}{%
+\subsection{Integration}\label{integration}}
+
+\[\int f(x) dx = F(x) + c\]
+
+% \begin{itemize}
+% \tightlist
+% \item
+ area enclosed by curves
+% \end{itemize}
+
+\tablehead{\hline \(f(x)\) & \(\int f(x) \cdot dx\) \\ \hline \\}
+\begin{supertabular}[]{@{}ll@{}}
+
+
+\(k\) (constant) & \(kx + c\) \\
+\(x^n\) & \({1 \over {n+1}}x^{n+1} + c\) \\
+\(a x^{-n}\) & \(a \cdot \log_e x + c\) \\
+\(e^{kx}\) & \({1 \over k} e^{kx} + c\) \\
+\(e^k\) & \(e^kx + c\) \\
+\(\sin kx\) & \(-{1 \over k} \cos (kx) + c\) \\
+\(\cos kx\) & \({1 \over k} \sin (kx) + c\) \\
+\({f^\prime (x)} \over {f(x)}\) & \(\log_e f(x) + c\) \\
+\(g^\prime(x)\cdot f^\prime(g(x)\) & \(f(g(x))\) (chain rule) \\
+\(f(x) \cdot g(x)\) & \(\int [f^\prime(x) \cdot g(x)] dx + \int [g^\prime(x) f(x)] dx\) \\
+\({1 \over {ax+b}}\) & \({1 \over a} \log_e (ax+b) + c\) \\
+\((ax+b)^n\) & \({1 \over {a(n+1)}}(ax+b)^{n-1} + c\) \\
+
+\end{supertabular}
+
+\hypertarget{definite-integrals}{%
+\subsection{Definite integrals}\label{definite-integrals}}
+
+\[\int_a^b f(x) \cdot dx = [F(x)]_a^b=F(b)-F(a)_{}\]
+
+\hypertarget{kinematics}{%
+\subsection{Kinematics}\label{kinematics}}
+
+\textbf{position \(x\)} - distance from origin or fixed point\\
+\textbf{displacement \(s\)} - change in $x$ from starting point \\
+\textbf{velocity \(v\)} - change in position with respect to time\\
+\textbf{acceleration \(a\)} - change in velocity\\
+\textbf{speed} - magnitude of velocity
+
+\large{
+\tablehead{}
+\begin{supertabular}[]{@{}ll@{}}
+% \toprule
+& no\tabularnewline
+\(v=u+at\) & \(s\)\tabularnewline
+\(s=ut + {1 \over 2} at^2\) & \(v\)\tabularnewline
+\(v^2 = u^2 + 2as\) & \(t\)\tabularnewline
+\(s= {1 \over 2}(u+v)t\) & \(a\)\tabularnewline
+
+
+
+\end{supertabular}
+}
+% \end{multicols}
+\end{document}