Multiple alignments of equations

Question

I have three equations of different lengths, each having alignments within them (at the '=' and'+') sign. However, I also want to align the three equations at the first '=' of each equation (marked in yellow in the picture below) and also maintain the space between them ,which is produced by the three align environments.

 \documentclass{article}

 \usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}

\begin{document}
\begin{align*}
\frac{\partial F(\phi)}{\partial \beta_1}  &=  \sum_{i: x_i =0} y_i .... \\
&\mathrel{\phantom{=}} + \sum_{i: y_i > 0} 2y_i + ab
\end{align*}
\begin{align*}
\frac{\partial F(\phi)}{\partial \beta_2} &=  \sum_{i: x_i =0} y_i + 2y_{i}^{2} \\
&\mathrel{\phantom{=}} + \sum_{i: y_i > 0} 2y_i + ab + 2x
\end{align*}
\begin{align*}
\frac{\partial F(\phi)}{\partial \beta_3} &=  \sum_{i: x_i =0} y_i + (y+1)^2 - (y-1)^2 \\
&\mathrel{\phantom{=}} + \sum_{i: y_i > 0} 2y_i + ab
\end{align*}
\end{document}

I have tried it by using the alignat command but I did not manage to obtain the result I want . The result at the moment looks like

Answer 1

I think the simplest way to achieve what you want is really to use a single align* environment. Then you can manually add some extra spacing between the three expressions in the optional argument of \\, when switching lines.

\documentclass{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}

\begin{document}
\begin{align*}
\frac{\partial F(\phi)}{\partial \beta_1}  &=  \sum_{i: x_i =0} y_i .... \\
&\mathrel{\phantom{=}} + \sum_{i: y_i > 0} 2y_i + ab \\[4mm]
\frac{\partial F(\phi)}{\partial \beta_2} &=  \sum_{i: x_i =0} y_i + 2y_{i}^{2} \\
&\mathrel{\phantom{=}} + \sum_{i: y_i > 0} 2y_i + ab + 2x \\[4mm]
\frac{\partial F(\phi)}{\partial \beta_3} &=  \sum_{i: x_i =0} y_i + (y+1)^2 - (y-1)^2 \\
&\mathrel{\phantom{=}} + \sum_{i: y_i > 0} 2y_i + ab
\end{align*}
\end{document}

Answer 2

In addition to employing a single align* environment, I would also like to recommend that you encase all six \sum terms in \smashoperator "wrappers" to achieve a more compact appearance of the equations. (Basically, the \smashoperator directives let the summation subscript terms protrude to the left and right without this messing up the spacing to the left and right of the \sum symbols.) I would also replace all instances of &\mathrel{\phantom{=}} with either &\quad or &\qquad.

\documentclass{article}
\usepackage{amssymb,amsthm}
\usepackage{mathtools} % 'mathtools' loads 'amsmath' automatically

\begin{document}
\begin{align*}
\frac{\partial F(\phi)}{\partial \beta_1}  
  &=       \smashoperator{\sum_{i: x_i =0}} y_i \dots \\
  &\qquad+ \smashoperator{\sum_{i: y_i > 0}} 2y_i + ab \\[\jot]
\frac{\partial F(\phi)}{\partial \beta_2} 
  &=       \smashoperator{\sum_{i: x_i =0}} y_i + 2y_{i}^{2} \\
  &\qquad+ \smashoperator{\sum_{i: y_i > 0}} 2y_i + ab + 2x \\[\jot]
\frac{\partial F(\phi)}{\partial \beta_3} 
  &=       \smashoperator{\sum_{i: x_i =0}} y_i + (y+1)^2 - (y-1)^2 \\
  &\qquad+ \smashoperator{\sum_{i: y_i > 0}} 2y_i + ab
\end{align*}
\end{document}

Answer 3

Based on @Mico's nice answer (+1) but with use of \pdv of derivative package and multlined environment, \smashoperator and \mathrlap of mathtools package:

\documentclass{article}

\usepackage{amssymb, amsthm}
\usepackage{mathtools}  % it load amsmath too
\usepackage{derivative}

\begin{document}
    \begin{align*}
\pdv{F(\phi)}{\beta_1}  
    & = \begin{multlined}[t]
        \smashoperator{\sum_{i:x_i=0}}  \mathrlap{y_i \dots} \\
            + \smashoperator{\sum_{i:y_i>0}}    2y_i + ab
        \end{multlined}     \\[\jot]
%
\pdv{F(\phi)}{\beta_2}
    & = \begin{multlined}[t]
        \smashoperator{\sum_{i:x_i=0}}  \mathrlap{y_i + 2y_{i}^{2}} \\
            + \smashoperator{\sum_{i:y_i>0}}    2y_i + ab + 2x
        \end{multlined}     \\[\jot]
%
\pdv{F(\phi)}{\beta_3}
    & = \begin{multlined}[t]
        \smashoperator{\sum_{i:x_i=0}}  \mathrlap{y_i + (y+1)^2 - (y-1)^2} \\
            + \smashoperator{\sum_{i:y_i>0}}    2y_i + ab
        \end{multlined}
    \end{align*}
\end{document}

Answer 4

Use the IEEEtrantools package. Effortless alignment of multiple and complex equations. Separate multiple eqns with \\ and use \begin{IEEEeqnarray}{} and \end{IEEEeqnarray}. Three alignment choices in the begin bracket.

\documentclass[letterpaper, 10pt]{memoir}  
\usepackage{graphicx}     
\usepackage{amsmath}   
\usepackage[retainorgcmds]{IEEEtrantools} %for aligning eqns with multiple lines  

\begin{document}

\begin{IEEEeqnarray}{rCl}
  
\overline{C_2B} &=& r = \dfrac{\sqrt {9\Phi^{2}+1} }{2}\,tis.\nonumber \\\  

\overline{BX} &=& \mbox{midface of pentagon to a vertex of pentagon} = \dfrac{\Phi}{\sqrt {\Phi^{2}+1} }\,tis. \nonumber \\\

h^{2} &=& \overline {C_{2} B}^{2}-\overline {BX} 
^{2}=\dfrac{9\Phi^{2}+1}{4}-\dfrac{\Phi^{2}}{\Phi^{2}+1}\nonumber \\\ 

&=& \dfrac{(\Phi^{2}+1)(9\Phi^{2}+1)-4\Phi^{2}}{4(\Phi 
^{2}+1)}\nonumber \\\

&=&\dfrac{9\Phi^{4}+6\Phi^{2}+1}{4(\Phi 
^{2}+1)}=\dfrac{(3\Phi^{2}+1)^{2}}{4(\Phi^{2}+1)}\nonumber \\\ 

h &=& \dfrac{3\Phi^{2}+1}{2\sqrt {\Phi^{2}+1} }\,tis=2.327438437\,tis.
  
\end{IEEEeqnarray} 

Looks like this:

The same equations with change in the first parameter from {rCl} to {cCl}centers the left side of each equation

\begin{IEEEeqnarray}{cCl}

The same equations with change in the first parameter from {lCl} to {lCl} moves the left side of each equation all the way to the left

\begin{IEEEeqnarray}{lCl}

This system is very flexible and allows the alignment of eqns pretty much where you want them.