3 vertical points between three equations that are lined up

Question

I'm trying to put vertical lines between the equations, but I can't do it. Here's my MWE.

\begin{align}
\frac{dx_1}{dt} &= f_1&(x_1,\dots,x_i, x_n)\\
\vdots & &\vdots \\
\frac{dx_i}{dt} &= f_i&(x_1,\dots,x_i, x_n)\\
\vdots & &\vdots \\
\frac{dx_n}{dt} &= f_n&(x_1,\dots,x_i, x_n)
\end{align}

The dots are not in the right place. I want centered dots in both sides.

Answer 1

The magic word is \vdotswithin{...}. It horizontally centers \vdots in a box of the same width as .... Note that the \vdots in the first column are centered within the = which I consider better than within the whole expression.

Furthermore I'd recommend to not number the even lines (\nonumber). And there is another version of \vdotswithin, namely \shortvdotswithin, but this will cause a linebreak and therefore you cannot use it in this case, unless you don't use the workaround described in the mathtools documentation.

\documentclass{article}
\usepackage{mathtools}

\begin{document}
    \newlength{\mylengthA} \settowidth{\mylengthA}{$\dfrac{dx_i}{dt}$}
    \begin{align}
        \frac{dx_1}{dt} &= f_1           & &(x_1,\dots,x_i, x_n)               \\
                        &\vdotswithin{=} & &\vdotswithin{(x_1,\dots,x_i, x_n)} \\
        \frac{dx_i}{dt} &= f_i           & &(x_1,\dots,x_i, x_n)               \\
                        &\vdotswithin{=} & &\vdotswithin{(x_1,\dots,x_i, x_n)} \\
        \frac{dx_n}{dt} &= f_n           & &(x_1,\dots,x_i, x_n)
    \end{align}
\end{document}