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12
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'table of derivatives'
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| Title of object: |
table of derivatives |
| Canonical Name: |
TableOfDerivatives |
| Type: |
Feature |
| Created on: |
2007-10-12 12:08:15 |
| Modified on: |
2007-10-18 12:02:15 |
| Classification: |
msc:26A24 |
Revision comment (for changes between this and next version):
Preamble:
\usepackage{amssymb,amscd}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{tabls}
% used for TeXing text within eps files
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
\usepackage{amsthm}
% making logically defined graphics
\usepackage{xypic}
\usepackage{pst-plot}
\usepackage{psfrag}
% define commands here
\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{ex}{Example}
\newcommand{\real}{\mathbb{R}}
\newcommand{\ints}{\mathbb{Z}}
\newcommand{\pdiff}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\mpdiff}[3]{\frac{\partial^#1 #2}{\partial #3^#1}} |
Content:
\PMlinkescapeword{mode}
\PMlinkescapeword{open}
\PMlinkescapeword{line}
\PMlinkescapeword{lines}
\PMlinkescapeword{code}
Below is a table of some real-valued functions and their corresponding derivatives:
\begin{center}
\begin{tabular}{|c|c|}
\hline\hline
$f(x)$ & $\displaystyle{\frac{df(x)}{dx}} = f'(x)$ \\
\hline\hline
$f(x) + g(x)$ & $f'(x)+g'(x)$\\
\hline
$f(x)g(x)$ & $f'(x)g(x)+f(x)g'(x)$\\
\hline
$\displaystyle \frac{f(x)}{g(x)},\, g\neq 0$ & $\displaystyle \frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}$\\
\hline
$f(g(x))$&$f'(g(x))g'(x)$\\
\hline
$c\in \mathbb{R}$ & 0 \\
\hline
$x^r$ & $rx^{r-1}$ \\
\hline
$a^x$&$a^x\ln{a}$\\
\hline
$\exp(x)=e^x$ & $\exp(x)=e^x$\\
\hline
$\ln x$ & $\displaystyle{\frac{1}{x}}$ \\
\hline
$\sin{x}$ & $\cos{x}$\\
\hline
$\cos{x}$ & $-\sin{x}$\\
\hline
$\sinh{x}$&$\cosh{x}$\\
\hline
$\cosh{x}$&$\sinh{x}$\\
\hline
% add your function here & add its derivative here \\
% \hline
\end{tabular}
\end{center}
\textbf{Instructions on how to add a function and its derivative}. Open the entry in edit mode. Make a copy of the two lines of comment (starting with \%) in the code (within the tabular environment), and paste it immediately before the comment. Uncomment the lines (take out the \% symbols) after completing. Preview before saving the entry. |
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