#+TITLE:Table of Derivatives
#+SETUPFILE: ../math_options.org
#+LATEX_HEADER: \usepackage{bm}
#+LATEX_HEADER: \usepackage{mathtools}
#+LATEX_HEADER: \newcommand{\dcoff}[1]{\frac{\text{d}}{\text{d}x} #1}
#+LATEX_HEADER: \newcommand{\sdcoff}[1]{\frac{\text{d}#1}{\text{d}x}}
#+LATEX_HEADER: \newcommand{\deriv}[2]{\frac{\text{d}}{\text{d}x} #1 &= #2}

* Disclaimer
This site as of now just a technology demonstration and its claims
should not be taken as true (even though I myself am pretty confident
they are)

* General Properties of the Derivative
Let $f$ and $g$ be real valued functions and $c$ some real constant:
\begin{align*}
\dcoff{(cf)} &= c\sdcoff{f}\\
\dcoff{(f \pm g)} &= \sdcoff{f} \pm \sdcoff{g}\\
\dcoff{(fg)} &= \sdcoff{f}g + f\sdcoff{g}\\
\dcoff{\left(\frac{f}{g}\right)} &= \frac{\sdcoff{f}g - f\sdcoff{g}}{g^2}
\end{align*}

* Trigonometric Funtions
\begin{align*}
\deriv{\sin(x)}{\cos(x)}\\
\deriv{\cos(x)}{-\sin(x)}\\
\deriv{\tan(x)}{\sec^2(x)}\\
\deriv{\sec(x)}{\sec(x)\tan(x)}\\
\deriv{\csc(x)}{\csc(x)\cot(x)}\\
\deriv{\csc(x)}{-\csc^2(x)}
\end{align*}