% http://tex.stackexchange.com/q/350028/
\documentclass{book}
\usepackage[T1]{fontenc}
\usepackage{xsim}
\usepackage[most]{tcolorbox}
\tcbuselibrary{skins,breakable}

\DeclareExerciseEnvironmentTemplate{tcolorbox}
  {%
    \tcolorbox[
      enhanced,
      colframe=green!20!black,
      colback=yellow!10!white,
      coltitle=green!40!black,
      fonttitle=\bfseries,
      underlay={%
        \begin{tcbclipinterior}
          \shade[
            inner color=\IfInsideSolutionTF{red!50!yellow}{green!80!yellow},
            outer color=yellow!10!white]
            (interior.north west) circle (2cm);
          \draw[help lines,step=5mm,yellow!80!black,shift={(interior.north west)}]
            (interior.south west) grid (interior.north east);
          \end{tcbclipinterior}%
        },
      attach title to upper=\quad,
      title = \XSIMmixedcase{\GetExerciseName}~\GetExerciseProperty{counter}
      \IfExercisePropertySetT{points}{%
        (\GetExerciseProperty{points}
        \IfExerciseGoalSingularTF{points}
          {\XSIMtranslate{point}}
          {\XSIMtranslate{points}})%
      }]%
    \IfInsideSolutionT{\label{solution:\ExerciseID}}%
  }
  {%
    \endtcolorbox
    \vspace*{\baselineskip}
    \IfInsideSolutionTF
      {%
        \noindent Exercise~\GetExerciseProperty{counter} is on
        page~\GetExerciseProperty{page}.%
      }
      {%
        \noindent The solution of this exercise is on
        page~\pageref{solution:\ExerciseID}.%
      }%
    \vspace{\baselineskip}
  }

\xsimsetup{
  exercise/template = tcolorbox ,
  solution/template = tcolorbox
}

\usepackage{fmtcount,etoolbox}
\newrobustcmd*\mystringnum[2]{\csname#1stringnum\endcsname{#2}}
\renewcommand*\thechapter{\mystringnum{number}{\value{chapter}}}
\renewcommand*\thesection{\arabic{chapter}.\arabic{section}}

% for the header: \MakeUppercase{\mystringnum{number}{1}}
%                 => \mystringnum{NUMBER}{1}
%                 => \NUMBERstringnum{1}
% elsewhere:      \mystringnum{number}{1}
%                 => \numberstringnum{1}

\usepackage{totcount}
\regtotcounter{chapter}

\newcounter{chapters}
\setcounter{chapters}{1}
\newcommand*\printsolutionsperchapter{%
  \whileboolexpr
    { test { \ifnumless {\value{chapters}} {\totvalue{chapter}+1} } }
    {%
      \printsolutions[chapter=\value{chapters},headings-template=per-chapter]
      \stepcounter{chapters}%
    }%
}

\begin{document}

\chapter{The First Chapter}

\begin{exercise}
  Compute the derivative of the following function:
  \begin{equation*}
    f(x) = \sin((\sin x)^2)
  \end{equation*}
\end{exercise}
\begin{solution}
  The derivative is:
  \begin{align*}
    f’(x) &= ( \sin((\sin x)^2) )'
           = \cos((\sin x)^2) \cdot 2\sin x \cos x
  \end{align*}
\end{solution}

\begin{exercise}
  Compute the derivative of the following function:
  \begin{equation*}
    f(x) = \sin((\sin x)^2)
  \end{equation*}
\end{exercise}
\begin{solution}
  The derivative is:
  \begin{align*}
    f’(x) &= ( \sin((\sin x)^2) )'
           = \cos((\sin x)^2) \cdot 2\sin x \cos x
  \end{align*}
\end{solution}

\chapter{The Second Chapter}

\begin{exercise}
  Compute the derivative of the following function:
  \begin{equation*}
    f(x) = (x^2+1) \sqrt{x^4+1}
  \end{equation*}
\end{exercise}
\begin{solution}
  The derivative is:
  \begin{align*}
    f’(x) &= ( (x^2+1) \sqrt{x^4+1} )'
           = 2x\sqrt{x^4+1} + \frac{2x^3(x^2+1)}{\sqrt{x^4+1}}
  \end{align*}
\end{solution}

\clearpage
\section{Solutions of the Exercices}

\printsolutionsperchapter

\end{document}
