Design a multiple columns environment to arrange exercises

Question

I want write the code like:

...
    \item
    \textbf{Differentiation}.

    Differentiate with respect to $x$:
    \begin{exercises}{3}
        \item$x^{2} - 3x$.
        \item$x^{5} - \dfrac{x^3}{3}$.
        \item$x + \dfrac{1}{x}$.
        ...
    \end{exercises}

    \item
    Differentiate with respect to $x$:
        \begin{exercises}{2}
        \item$y = x\cos\frac{1}{2}x$.
        \item$y = \sin\left(\dfrac{\pi x}{180}\right)$.
        \item$y = \frac{x^2}{1+x}$.
        ...
        \end{exercises}
    ...
...

But if I use shortlst package as an advice from An environment which be used to arrange exercises mostly similiar with common enumerate list, the content after second \item Differentiate with respect to $x$ in pic above will typeset in three columns.

----EDIT---- The proposal that use a minipage environment is restricted with the minipage's width defined in advance, that say, it is not suit for different page width. change

\documentclass{article}
\usepackage{shortlst}
\usepackage[width=10cm]{geometry}
\usepackage{lipsum}
\begin{document}
\lipsum[1]
\newenvironment{exercises}[1]
    {#1:\\ \begin{minipage}[t]{0.9\textwidth}\begin{shortenumerate}}
    {\end{shortenumerate}\end{minipage}}
\begin{enumerate}
\item
\begin{exercises}{\textbf{Differentiation}\\ Differentiate with respect to $x$}
     \item $x^3-3x$
     \item $x^5-\frac{x^3}{3}$
     \item $x+\frac{1}{x}$
     \item $(x+1)^2(x-1)^2$
     \item $x\sin x$
\end{exercises}
\item
\begin{exercises}{Differentiate with respect to $x$}
     \item $y=x\cos \frac{1}{2}x$
     \item $y=\sin\left(\frac{\pi x}{180}\right)$
     \item $y=\frac{x^2}{1+x}$ 
\end{exercises}
\end{enumerate}
\end{document}

to

\documentclass{article}
\usepackage{shortlst}
\usepackage[width=9cm]{geometry}
\usepackage{lipsum}
\begin{document}
\lipsum[1]
\newenvironment{exercises}[1]
    {#1:\\ \begin{minipage}[t]{0.9\textwidth}\begin{shortenumerate}}
    {\end{shortenumerate}\end{minipage}}
\begin{enumerate}
\item
\begin{exercises}{\textbf{Differentiation}\\ Differentiate with respect to $x$}
     \item $x^3-3x$
     \item $x^5-\frac{x^3}{3}$
     \item $x+\frac{1}{x}$
     \item $(x+1)^2(x-1)^2$
     \item $x\sin x$
\end{exercises}
\item
\begin{exercises}{Differentiate with respect to $x$}
     \item $y=x\cos \frac{1}{2}x$
     \item $y=\sin\left(\frac{\pi x}{180}\right)$
     \item $y=\frac{x^2}{1+x}$ 
\end{exercises}
\end{enumerate}
\end{document}

will get

so is the code given by Schweinebacke unless I changed the width individually

\documentclass{article} 
\usepackage{shortlst}% http://ctan.org/pkg/shortlst 
\usepackage{scrextend} 
\usepackage{lipsum} 
\usepackage[width=10cm]{geometry} %added
\begin{document} 

\lipsum[1] 
\begin{enumerate} 
\item {Differentiate with respect to $x$: 
  \begin{addmargin}[0pt]{0.1\linewidth} 
    \begin{shortenumerate} 
      \item $x^3-3x$  
      \item $x^5-\frac{x^3}{3}$ 
      \item $x+\frac{1}{x}$ 
      \item $(x+1)^2(x-1)^2$ 
      \item $x\sin x$ 
    \end{shortenumerate} 
  \end{addmargin} 
} 
\item {Differentiate with respect to $x$: 
  \begin{addmargin}[0pt]{.4\linewidth} 
    \begin{shortenumerate} 
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
    \end{shortenumerate} 
  \end{addmargin} 
} 
\end{enumerate} 
\end{document}

Answer 1

The result of your earlier question, possibly in a minipage, and an ordinary enumeration environment should get the result you want.

\documentclass{article}
\usepackage{shortlst}% http://ctan.org/pkg/shortlst
\begin{document}

\newenvironment{exercises}[1]
    {#1:\\ \begin{minipage}[t]{0.9\textwidth}\begin{shortenumerate}}
    {\end{shortenumerate}\end{minipage}}

\begin{enumerate}
\item 
\begin{exercises}{\textbf{Differentiation}\\ Differentiate with respect to $x$}
     \item $x^3-3x$ 
     \item $x^5-\frac{x^3}{3}$
     \item $x+\frac{1}{x}$
     \item $(x+1)^2(x-1)^2$
     \item $x\sin x$
\end{exercises}
\item 
\begin{exercises}{Differentiate with respect to $x$}
     \item $x^3-3x$ 
     \item $x^5-\frac{x^3}{3}$
     \item $x+\frac{1}{x}$
     \item $(x+1)^2(x-1)^2$
     \item $x\sin x$
\end{exercises}
\end{enumerate}

\end{document}

which looks like

If you want a table like environment to handle a specific number of columns of equations, then you can define a new counter to do this.

\newcounter{innerlist} 
\renewcommand{\theinnerlist}{\arabic{innerlist}} 
\newcommand{\inneritem}[1]{\refstepcounter{innerlist}\theinnerlist.\ #1}

\newenvironment{exercises}[2]
    {\setcounter{innerlist}{0}\begin{minipage}[t]{0.9\textwidth}#1:\\ \begin{tabular}{#2}}
    {\end{tabular}\end{minipage}}


\begin{enumerate}
    \item 
    \begin{exercises}{\textbf{Differentiation}\\ Differentiate with respect to $x$}{ll}
        \inneritem{$x^3-3x$} & \inneritem{$x^5-\frac{x^3}{3}$}\\
        \inneritem{$x+\frac{1}{x}$} & \inneritem{$(x+1)^2(x-1)^2$}\\
        \inneritem{$x\sin x$} & \inneritem{$x\sin x$}
    \end{exercises}
    \item
    \begin{exercises}{\textbf{Differentiation}\\ Differentiate with respect to $x$}{lll}
        \inneritem{$x^3-3x$} & \inneritem{$x^5-\frac{x^3}{3}$} & \inneritem{$x+\frac{1}{x}$}\\
        \inneritem{$(x+1)^2(x-1)^2$} & \inneritem{$x\sin x$} & \inneritem{$x\sin x$}
    \end{exercises}
\end{enumerate}

This version shouldn't have any big issues spreading over pages. Each minipage shouldn't spread between pages, but the items in the outer enumerated list will spread fine.

An alteration using the longtables package allows this to run over pages:

\newenvironment{exercises}[2]
    {\setcounter{innerlist}{0}#1:\\ \begin{longtable}[t]{#2}}
    {\end{longtable}}

Answer 2

I would suggest to combine Mark's answer with package scrextend. That would support page breaks inside the exercise:

\documentclass{article}
\usepackage{shortlst}% http://ctan.org/pkg/shortlst
\usepackage{scrextend}
\usepackage{lipsum}
\begin{document}

\lipsum[1-4]
\begin{enumerate}
\item {Differentiate with respect to $x$:
  \begin{addmargin}[0pt]{2em}
    \begin{shortenumerate}
      \item $x^3-3x$ 
      \item $x^5-\frac{x^3}{3}$
      \item $x+\frac{1}{x}$
      \item $(x+1)^2(x-1)^2$
      \item $x\sin x$
    \end{shortenumerate}
  \end{addmargin}
}
\item {Differentiate with respect to $x$:
  \begin{addmargin}[0pt]{2em}
    \begin{shortenumerate}
      \item $y=x\cos \frac{1}{2}x$
      \item $y=\sin\left(\frac{\pi x}{180}\right)$
      \item $y=\frac{x^2}{1+x}$
      \item $y=x\cos \frac{1}{2}x$
      \item $y=\sin\left(\frac{\pi x}{180}\right)$
      \item $y=\frac{x^2}{1+x}$
      \item $y=x\cos \frac{1}{2}x$
      \item $y=\sin\left(\frac{\pi x}{180}\right)$
      \item $y=\frac{x^2}{1+x}$
      \item $y=x\cos \frac{1}{2}x$
      \item $y=\sin\left(\frac{\pi x}{180}\right)$
      \item $y=\frac{x^2}{1+x}$
    \end{shortenumerate}
  \end{addmargin}
}
\end{enumerate}
\end{document}

Note: If you're already using a KOMA-Script class you don't need to load the package scrextend.

You may define an enviroment for this:

\documentclass{article}
\usepackage{shortlst}% http://ctan.org/pkg/shortlst  
\usepackage{scrextend}
\usepackage{lipsum}% 
\usepackage[width=10cm]{geometry} %added

\newenvironment{exercise}[1][\strut]{%
  \item #1\begin{addmargin}[0pt]{2em}\begin{shortenumerate} 
}{%
  \end{shortenumerate}\end{addmargin} 
}
\begin{document} 

\lipsum[1] 
\begin{enumerate}
  \begin{exercise}[{Differentiate with respect to $x$:}]
  \item $x^3-3x$  
  \item $x^5-\frac{x^3}{3}$ 
  \item $x+\frac{1}{x}$ 
  \item $(x+1)^2(x-1)^2$ 
  \item $x\sin x$ 
  \end{exercise}
  \begin{exercise}[{Differentiate with respect to $x$:}]
  \item $y=x\cos \frac{1}{2}x$ 
  \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
  \item $y=\frac{x^2}{1+x}$ 
  \item $y=x\cos \frac{1}{2}x$ 
  \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
  \item $y=\frac{x^2}{1+x}$ 
  \item $y=x\cos \frac{1}{2}x$ 
  \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
  \item $y=\frac{x^2}{1+x}$ 
  \item $y=x\cos \frac{1}{2}x$ 
  \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
  \item $y=\frac{x^2}{1+x}$ 
  \end{exercise} 
\end{enumerate} 
\end{document}

Answer 3

You could use a combination of multicols with a newlist using the enumitem package, as demonstrated below.

It allows pagebreaks too.

\documentclass{article} 
\usepackage{lipsum} 
\usepackage{multicol}             % multicols
\usepackage{enumitem}             % customized lists
\usepackage[width=10cm]{geometry} % page dimensions

% setup a new list (terminology from enumitem)
\newlist{mylist}{enumerate}{5}
\setlist[mylist]{label=(\alph*)}

\newenvironment{exercises}[1]{\begin{multicols}{#1}\begin{mylist}}{\end{mylist}\end{multicols}}

\begin{document} 

\vspace*{4cm}   % purely to demonstrate the pagebreak
\lipsum[1-2] 

\begin{enumerate} 
 \item {Differentiate with respect to $x$:}
  \begin{exercises}{2}
      \item $x^3-3x$  
      \item $x^5-\frac{x^3}{3}$ 
      \item $x+\frac{1}{x}$ 
      \item $(x+1)^2(x-1)^2$ 
      \item $x\sin x$ 
  \end{exercises} 
 \item Differentiate with respect to $x$:
 \begin{exercises}{2}
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
      \item $y=x\cos \frac{1}{2}x$ 
      \item $y=\sin\left(\frac{\pi x}{180}\right)$ 
      \item $y=\frac{x^2}{1+x}$ 
  \end{exercises} 
\end{enumerate} 
\end{document}

Answer 4

Here is another solution using the {tasks} environment provided by the exsheets package. There is at least one downside to it, though: it cannot safely be nested with other {tasks} environments. (It is not a real list in the LaTeX sense although the syntax is similar.)

The environment has an optional argument that specifies the number of columns:

\begin{tasks}{<num of cols>}
 \task first item
 \task second item
 ...
\end{tasks}

Here is the full example:

\documentclass{article}
\usepackage[load-headings]{exsheets}

\SetupExSheets{
  % first the number then the title:
  headings=block-rev,
  % number tasks (a), (b), ...
  tasks/label=(tsk[a]),
  % make sure the task item labels have enough space:
  tasks/label-width=2em
}
\usepackage{lipsum}% dummy text

\begin{document} 

\lipsum[1]\bigskip

\begin{question}[name=Differentiation]
 Differentiate with respect to $x$: 
 \begin{tasks}{3}% three columns
   \task $x^3-3x$  
   \task $x^5-\frac{x^3}{3}$ 
   \task $x+\frac{1}{x}$ 
   \task $(x+1)^2(x-1)^2$ 
   \task $x\sin x$
 \end{tasks}
\end{question}

\begin{question}[name=More Differentiation]
 Differentiate with respect to $x$: 
 \begin{tasks}{2}% two columns
   \task $y=x\cos \frac{1}{2}x$ 
   \task $y=\sin\left(\frac{\pi x}{180}\right)$ 
   \task $y=\frac{x^2}{1+x}$ 
   \task $y=x\cos \frac{1}{2}x$ 
   \task $y=\sin\left(\frac{\pi x}{180}\right)$ 
   \task $y=\frac{x^2}{1+x}$ 
   \task $y=x\cos \frac{1}{2}x$ 
   \task $y=\sin\left(\frac{\pi x}{180}\right)$ 
   \task $y=\frac{x^2}{1+x}$ 
   \task $y=x\cos \frac{1}{2}x$ 
   \task $y=\sin\left(\frac{\pi x}{180}\right)$ 
   \task $y=\frac{x^2}{1+x}$ 
 \end{tasks}
\end{question}

\end{document}