From 561bac75579391c14e47eaccfabdf9eda98855da Mon Sep 17 00:00:00 2001
From: Thomas Albers <thomas@thomaslabs.org>
Date: Wed, 27 Jul 2022 18:13:20 +0200
Subject: Initial commit

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 math/derivatives.org | 31 +++++++++++++++++++++++++++++++
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+#+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*}
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