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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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