Linking top of tree to one node

Question

having got very useful help to my posts here and here I have been able to find a number of documents on drawing trees. However it is taking me time to link all the nodes at the top of the tree (at the bottom since the tree is growing down) into one node. I would appreciate a quick fix of this, if what am trying to do is possible. In the mwe below I want to have only one node from x and y, to x

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

\begin{tikzpicture}[inner sep=1.5pt]
\node (10) {z=F(x,y)}
[ 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 {x}
      edge from parent node[swap]{$\frac{dx}{dx}=1$}
    }
    edge from parent node[swap]{$\frac{\partial z}{\partial x}=F_{x}$}
  }
  child { node {y}
    child { node {x}
      edge from parent node{$\frac{dy}{dx}$}
    }
    edge from parent node{$\frac{\partial z}{\partial y}=F_{y}$}
}
;
\end{tikzpicture}
\end{document}

Answer 1

For a diagram like that I wouldn't use a tree at all. Instead, I'd use tikz-cd.

\documentclass[12pt]{report}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}[row sep=1.5cm,column sep=0.3cm,every arrow/.append style={dash}]
& z=F(x,y)
  \arrow[ld,swap,"\frac{\partial z}{\partial x} = F_{x}"]
  \arrow[rd,"\frac{\partial z}{\partial y} = F_{x}"]
& \\
x
  \arrow[rd,swap, "\frac{dx}{dx} = 1"]
 & & y 
  \arrow[ld,"\frac{dy}{dx}"]
\\
& x & \\
\end{tikzcd}
\end{document}