From 61b5ce20f25c5785e41574998a12c6d06eb05a5e Mon Sep 17 00:00:00 2001
From: Thomas Albers <thomas@thomaslabs.org>
Date: Wed, 8 Mar 2023 23:43:00 +0100
Subject: Restructure build system and directory structures

---
 src/math/derivatives.org | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)
 create mode 100644 src/math/derivatives.org

(limited to 'src/math/derivatives.org')

diff --git a/src/math/derivatives.org b/src/math/derivatives.org
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+#+title:Table of Derivatives
+#+setupfile: ../../math_options.org
+
+* 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*}
+\ddx{\sin(x)} &= \cos(x)\\
+\ddx{\cos(x)} &= -\sin(x)\\
+\ddx{\tan(x)} &= \sec^2(x)\\
+\ddx{\sec(x)} &= \sec(x)\tan(x)\\
+\ddx{\csc(x)} &= \csc(x)\cot(x)\\
+\ddx{\csc(x)} &= -\csc^2(x)
+\end{align*}
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