Labels on node links in tikz

Question

While @cfr provided an excellent solution to my post here, I have a problem when I insert the code in my main document, though it works fine as a standalone document. It gives me the error: ! Illegal parameter number in definition of \pgfmath@expression, suggesting the error is at \end{forest}. While forest seems to be more convenient for tree-diagrams, I find it very difficult. It will take me time to be able sort out my problem of the forest package. I am therefore reproducing my mwe in tikz, with only the tree-diagram and where I want the labels (as commented out in my code).

\documentclass[12pt]{report}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[inner sep=1.5pt]
\node (10) {z}
child { node {x}
child { node {s}}
   child { node {t}}}
child { node {y}
child { node {s}}
child { node {t}}}
;
%    \node      (from z to x) {$\frac{\partial z}{\partial x}$};
%    \node      (from z to y) {$\frac{\partial z}{\partial y}$};
%    \node      (from x to s) {$\frac{\partial x}{\partial s}$};
%    \node      (from x to t) {$\frac{\partial x}{\partial t}$};
%    \node      (from y to s) {$\frac{\partial y}{\partial s}$};
%    \node      (from y to t) {$\frac{\partial y}{\partial t}$};

\end{tikzpicture}
\end{document}

Answer 1

Suggestion only with TikZ:

\documentclass[12pt]{report}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[inner sep=1.5pt]
\node (10) {z}
  [ auto,
    sibling distance=2.4cm,
    level distance=2cm,
    level 2/.append style={
      sibling distance=1.8cm,
      level distance=1.5cm
    },
    edge from parent/.append style={nodes={pos=.6}}
  ]
  child { node {x}
    child { node {s}
      edge from parent node[swap]{$\frac{\partial x}{\partial s}$}
    }
    child { node {t}
      edge from parent node{$\frac{\partial x}{\partial t}$}
    }
    edge from parent node[swap]{$\frac{\partial z}{\partial x}$}
  }
  child { node {y}
    child { node {s}
      edge from parent node[swap]{$\frac{\partial y}{\partial s}$}
    }
    child { node {t}
      edge from parent node{$\frac{\partial y}{\partial t}$}
    }
    edge from parent node{$\frac{\partial z}{\partial y}$}
}
;
\end{tikzpicture}
\end{document}