LaTex definitions (very common ones) which are very simple to use.

[DrWahoo]

Feel free to test out the code. I use these nearly anytime I load up a new file in LaTex. They are very simple and easy to use versus typing out the full latex command. \usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\newtheorem{definition}{Definition}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
%

% THIS IS THE PLACE FOR YOUR OWN DEFINITIONS
\newcommand{\oper}[3]{[#1#2](#3)}
\newcommand{\domain}[1]{\mathcal{D}(#1) \equiv H^1_0(0,1) \cap H^2(0,1)}
\newcommand{\R}{{\rm I\! R^3_+}}
\newcommand{\Rn}{{\rm I\! R^n}}
\newcommand{\Rtwo}{{\rm I\! R^2}}
\newcommand{\Rfour}{{\rm I\! R^4_+}}
\newcommand{\e}[1]{e^{-(#1-\,\gamma)^2}}
\newcommand{\iprod}[2]{\langle#1,#2\rangle}
\newcommand{\innprod}[3]{\langle#1,#2\rangle _#3}
\newcommand{\sD}{\mathcal{D}}
\newcommand{\rint}[2]{\int^{1}_{0}{#1} \,d{#2}}
\newcommand{\rrint}[3]{\int^{1}_{0}\int^{1}_{0}{#1} \,d{#2}\,d{#3}}
\newcommand{\der}[1]{\frac{d #1}{dt}}
\newcommand{\pder}[2]{ \frac{\partial#1}{\partial #2} }
\newcommand{\secpder}[2]{\frac{\partial^2 #1}{\partial #2^2}}
\newcommand{\rrrrint}[5]{\int^{1}_{0}\int^{1}_{0}\int^{1}_{0}\int^{1}_{0}{#1} \,d{#2}\,d{#3}\,d{#4}\,d{#5}}
\newcommand{\p}{p(x,\xi)}
\newcommand{\Sum}[2]{\sum^N_{j=1}#1#2}
\newcommand{\norm}[1]{\parallel #1 \parallel}
%
% boldface characters in mathematical formulas
\newcommand{\bff}{\mbox{\boldmath $f$}}
\newcommand{\bfc}{\mbox{\boldmath $c$}}
\newcommand{\bfl}{\mbox{\boldmath $l$}}
\newcommand{\bfn}{\mbox{\boldmath $n$}}
\newcommand{\bfu}{\mbox{\boldmath $u$}}
\newcommand{\bfx}{\mbox{\boldmath $x$}}
\newcommand{\bfy}{\mbox{\boldmath $y$}}
\newcommand{\bfa}{\mbox{\boldmath $\alpha$}}
\newcommand{\bfzero}{\mbox{\boldmath $0$}}
\newcommand{\bfcurl}{{\bf curl}} % curl of a vector field
\newcommand{\rmdiv}{{\rm div}} % divergence of a vector field
\newcommand{\eop}{\hfill $\sqcap\!\!\!\!\sqcup$} % end of proof

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I can include examples of the code and output if any users fine the definitions helpful.

 

[DrWahoo]

An example for the commands below are as follows:

will edit tomorrow, to tired tonight.\begin{document}
$\pder{x}{t} = \frac{x}{t}$
$\der{x} = \frac{dx}{dt}$
\end{document}