[Tex/LaTex] How to “align” the LyX aligned math environment

Question

I frequently use the aligned math environment in LyX to typeset my equations. However, if I want to save space on the page and set two equations simultaneously in the same aligned math environment, the second equation fails to "stay" straight (see image below).

What do I need to do in order to set the equalities in the right equation in a straight line, like the ones in the left equation?

I've tried the following: using other math environments, inserting blank spaces, adding more columns.

Answer 1

This is precisely what the alignat and alignat* environments are designed for: they allow you to vertically align multiple columns. (Just as with align and align*, alignat numbers each equation and alignat* doesn't number them.)

To align n columns, place them in \begin{alignat*}{n}...\end{alignat*}, and align each column with an & as usual. However, you also need an & to separate each column (as in an array or table), and in the first row, you should insert any extra space you need before this separator.

Here's the LaTeX code I have:

\documentclass{article}
\usepackage{amsmath}
% \dr{F}{x} produces δF/δx
% \hdr{2}{F}{x} produces δ²F/δ²x
\newcommand{\dr}[2]{\frac{\delta #1}{\delta #2}} 
\newcommand{\hdr}[3]{\frac{\delta^{#1} #2}{\delta^{#1} #3}}
\begin{document}
\begin{alignat*}{2}
% set spacing between columns in the first row
\dr{F}{x} &= ye^{x+y} + y^3 + 2xy - 1 \qquad\qquad & \dr{F}{y} &= ye^{x+y} + e^{x+y} + 3xy^2+ x^2\\
\hdr{2}{F}{x} &= ye^{x+y} + 2y                     & \hdr{2}{F}{y} &= ye^{x+y} + 2e^{x+y} + 6xy\\
\hdr{3}{F}{x} &= ye^{x+y}                          & \hdr{3}{F}{y} &= ye^{x+y} + 3e^{x+y}+ 6x\\
\hdr{4}{F}{x} &= ye^{x+y}                          & \hdr{4}{F}{y} &= ye^{x+y}+ 4e^{x+y}\\
&\vdots                                            & \vdots\\
\hdr{r}{F}{x} &= ye^{x+y}                          & \hdr{r}{F}{y} &= ye^{x+y} + re^{x+y}
\end{alignat*}
\end{document}

And here's the result.