Is there free software that can be used to generate a chain rule tree graph?

Question

I'm in multivariate calculus and we just finished up the chain rule. One of the methods for solving this is to produce a tree graph and traverse it. An example would be this tree graph taken from my notes in class.

As part of class we need to write a report and I will be typing it all out in Word. I want to be able to insert tables like this into my report. To do that I need to generate them somehow, where the output could be inserted into Word (an image most likely).

I am wondering if there is any free software that will allow me to generate a tree just as nice as the example that is relatively painless to use. Preferably most of the layout will be managed for me, I'd just need to define the number of nodes, names of the nodes, and the labels of the lines. The software doesn't need to take in equation input, I'm fine with having to name everything manually. I don't need to be able to show different colored lines to show transversal.

I also have access to Maple at my school labs and Mathematica Pi Edition on my Raspberry Pis. If there are no free tools to do this, is it possible to set up in either of them?

Another example, though less desirable, would be this example taken from Paul's Notes.

Answer 1

Well this is somewhat jenky (it's my first really big figure created with latex) but I think it could get the job done - if you have other specific chains I can create them for you, if you want a more in depth explanation of the code let me know, otherwise I tried to be verbose. Here's the output:

And the code:

\documentclass{standalone}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
\newcommand{\chainx}{0}
\newcommand{\chainy}{0}
\def\chainleft{(-1)}
\def\chainright{1}
\def\chainup{1}
\def\chaindown{(-1)}
\makeatletter
\newcommand{\movechainxy}[4]{%
\g@addto@macro\chainx{ + #3 * #2 * cos(#1)}
\g@addto@macro\chainy{ + #4 * #2 * sin(#1)}
}
\makeatother
\newcommand{\setchainxy}[2]{%
\renewcommand{\chainx}{#1}
\renewcommand{\chainy}{#2}
}
\newcommand{\chainlegs}[7]{%
\draw[#3, very thick] ({\chainx}, {\chainy}) -- ({\chainx - 2 * cos(#1)}, {\chainy - #2 * sin(#1)});
\draw[#4, very thick] ({\chainx}, {\chainy}) -- ({\chainx + 2 * cos(#1)}, {\chainy - #2 * sin(#1)});
\draw[fill, #6] ({\chainx}, {\chainy}) circle [radius=2pt];
\node[#5, #6] at ({\chainx}, {\chainy}) {#7};
}
\begin{document}
  \begin{tikzpicture}
    \chainlegs{30}{2}{RubineRed}{RubineRed}{above}{RubineRed}{$z$}
    \movechainxy{30}{2}{\chainleft}{\chaindown}
    \chainlegs{60}{2}{RubineRed}{gray}{left}{ProcessBlue}{$x$}

    \setchainxy{0}{0}
    \movechainxy{30}{2}{\chainright}{\chaindown}
    \chainlegs{60}{2}{RubineRed}{gray}{right}{ProcessBlue}{$y$}

    \movechainxy{60}{2}{\chainleft}{\chaindown}
    \draw[fill, SeaGreen] ({\chainx}, {\chainy}) circle [radius=2pt];
    \node[below, SeaGreen] at ({\chainx}, {\chainy}) {$s$};

    \movechainxy{60}{2}{\chainright}{\chainup}
    \movechainxy{60}{2}{\chainright}{\chaindown}
    \draw[fill, SeaGreen] ({\chainx}, {\chainy}) circle [radius=2pt];
    \node[below, SeaGreen] at ({\chainx}, {\chainy}) {$t$};

    \setchainxy{0}{0}
    \movechainxy{30}{2}{\chainleft}{\chaindown}
    \movechainxy{60}{2}{\chainleft}{\chaindown}
    \draw[fill, SeaGreen] ({\chainx}, {\chainy}) circle [radius=2pt];
    \node[below, SeaGreen] at ({\chainx}, {\chainy}) {$s$};

    \movechainxy{60}{2}{\chainright}{\chainup}
    \movechainxy{60}{2}{\chainright}{\chaindown}
    \draw[fill, SeaGreen] ({\chainx}, {\chainy}) circle [radius=2pt];
    \node[below, SeaGreen] at ({\chainx}, {\chainy}) {$t$};

    \setchainxy{0}{0}
    \movechainxy{30}{1}{\chainleft}{\chaindown}
    \node[above left] at ({\chainx}, {\chainy}) {$\frac{\partial z}{\partial x}$};
    \movechainxy{30}{1}{\chainleft}{\chaindown}

    \movechainxy{60}{1}{\chainleft}{\chaindown}
    \node[left] at ({\chainx}, {\chainy}) {$\frac{\partial x}{\partial s}$};
    \movechainxy{60}{1}{\chainright}{\chainup}
    \movechainxy{60}{1}{\chainright}{\chaindown}
    \node[right] at ({\chainx}, {\chainy}) {$\frac{\partial x}{\partial t}$};

    \setchainxy{0}{0}
    \movechainxy{30}{1}{\chainright}{\chaindown}
    \node[above right] at ({\chainx}, {\chainy}) {$\frac{\partial z}{\partial y}$};
    \movechainxy{30}{1}{\chainright}{\chaindown}

    \movechainxy{60}{1}{\chainleft}{\chaindown}
    \node[left] at ({\chainx}, {\chainy}) {$\frac{\partial y}{\partial s}$};
    \movechainxy{60}{1}{\chainright}{\chainup}
    \movechainxy{60}{1}{\chainright}{\chaindown}
    \node[right] at ({\chainx}, {\chainy}) {$\frac{\partial y}{\partial t}$};

  \end{tikzpicture}
\end{document}