Question

Macros \[\newcommand\dd[1]{\,\mathrm d#1} % infinitesimal
\newcommand\de[2]{\frac{\mathrm d #1}{\mathrm d#2}} % first order derivative
\newcommand\pa[2]{\frac{\partial #1}{\partial #2}} % partial derivative
\newcommand\den[3]{\frac{\mathrm d^#3 #1}{\mathrm d#2^#3}} % n-th derivative
\newcommand\pan[3]{\frac{\partial^#3 #1}{\partial#2^#3}} % n-th partial derivative

\dd x
\de yx
\pa yx
\den yxn
\pan yxn\]

Answer 1

```
\newcommand\Beta[2]{\operatorname B \left(#1,#2\right)} % Beta function of (m,n)
\Beta mn
```
\[\newcommand\Beta[2]{\operatorname B \left(#1,#2\right)} % Beta function of (m,n)
\Beta mn\]

Answer 2

```
\newcommand\intl[4]{\int\limits_{#1}^{#2}{#3}{\dd#4}} % integral _{a}^{b}{f(x)}\dd x
\newcommand\erf[1]{\operatorname{erf}\left(#1\right)} % Error function (#1)
\newcommand\erfi[1]{\frac2{\sqrt\pi}\intl{0}{#1}{e^{-u^2}}{u}} % Error function integral (#1)
\intl abfx\\
\erf x=\erfi x\\
\erf y=\erfi y\\
\erf z=\erfi z
```
\[\newcommand\intl[4]{\int\limits_{#1}^{#2}{#3}{\dd#4}} % integral _{a}^{b}{f(x)}\dd x
\newcommand\erf[1]{\operatorname{erf}\left(#1\right)} % Error function (#1)
\newcommand\erfi[1]{\frac2{\sqrt\pi}\intl{0}{#1}{e^{-u^2}}{u}} % Error function integral (#1)
\intl abfx\\
\erf x=\erfi x\\
\erf y=\erfi y\\
\erf z=\erfi z\]