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}
multicol
package?