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Diffstat (limited to 'math/derivatives.org')
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diff --git a/math/derivatives.org b/math/derivatives.org new file mode 100644 index 0000000..4d5d4be --- /dev/null +++ b/math/derivatives.org @@ -0,0 +1,31 @@ +#+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*} |