Can't change place of footer and header page numbers [duplicate]

Question

I'm using the command \pagestype{myheadings} to make sure that the page header contains nothing else that the page number.

However, I can't manage to make the page number of the first page of chapter to be displayed up in the page corner.

Here is a sample code of what I'm doing so far:

\documentclass[12pt,a4paper]{book}

\usepackage[T1]{fontenc}
\usepackage[french]{babel}

\pagestyle{myheadings}

\title{Test book}
\author{Someone}
\date{\today}

\usepackage{lipsum}  

\begin{document}
    \sloppy
    \maketitle
    
    \chapter{First chapter}
    \lipsum[1-100]
    
    \backmatter
    \tableofcontents
\end{document}

Best rgards!

Answer 1

The book class uses the plain page style for the first page of the chapter. Here is the definition in book.cls:

\newcommand\chapter{\if@openright\cleardoublepage\else\clearpage\fi
     ----------->>  \thispagestyle{plain}%    <<-----------
                    \global\@topnum\z@
                    \@afterindentfalse
                    \secdef\@chapter\@schapter}

There are at least two ways to change this.

Using the fancyhdr package and redefining the plain style (see pages 12-13 of the documentation).

\usepackage{fancyhdr}
\fancypagestyle{plain}{%
  \fancyhf{}%
  \fancyhead[LE,RO]{\thepage}%
  \renewcommand{\headrulewidth}{0pt}%
  \renewcommand{\footrulewidth}{0pt}%
  }

Via etoolbox:

\usepackage{etoolbox}
\patchcmd{\chapter}{plain}{myheadings}{}{}

In fact this is equivalent to

\makeatletter
\renewcommand\chapter{\if@openright\cleardoublepage\else\clearpage\fi
                    \thispagestyle{myheadings}%
                    \global\@topnum\z@
                    \@afterindentfalse
                    \secdef\@chapter\@schapter}
\makeatother