Array/tabular env. showing fractions directly in display mode and correctly spaced?

Question

In my Latex documents I usually include arrays and tables with fraction that always get crushed to their inline form, giving an unpleasant result. I know I could solve the issue by switching every \frac to \dfrac and adjusting the vertical spaces between lines manually, but I was wondering if there's a quicker and smarter way to solve this. I checked the array package but I didn't seem to find anything about this issue.

Here's a MWE of an array crushing fractions:

\documentclass{article}
\usepackage{amsmath, array}

\begin{document}

\begin{equation*}
\begin{array}{ll}
\frac{\partial T}{\partial \dot{x}}=m \dot{x}\quad \frac{d}{d t}\left(\frac{\partial T}{\partial \dot{x}}\right)=m \ddot{x}\quad \frac{\partial T}{\partial x}=0 \\
\frac{\partial T}{\partial \dot{y}}=m \dot{y}\quad \frac{d}{d t}\left(\frac{\partial T}{\partial \dot{y}}\right)=m \ddot{y}\quad \frac{\partial T}{\partial y}=0 \\
\frac{\partial T}{\partial \dot{z}}=m \dot{z}\quad \frac{d}{d t}\left(\frac{\partial T}{\partial \dot{z}}\right)=m \ddot{z}\quad \frac{\partial T}{\partial z}=0
\end{array}
\end{equation*}

\end{document}

EDIT: What I'm looking for (not sure it exists) is an environment, or a "declaration" valid through the whole environment, switching every math element to \displastyle, just like the \dcases environment for the regular \cases one.

Answer 1

If you use environments from the tabularray package for your arrays and tables, you can use mode=dmath for the cells which contain math. This will make them show up in display style.

A short example:

\documentclass{article}
\usepackage{tabularray}
\UseTblrLibrary{amsmath}
\begin{document}

\[
\begin{+array}{
  colspec={X},
  cells={mode=dmath}
}
\frac{1}{2}\\
\end{+array}
\]

\begin{tblr}{
  colspec={c},
  cells={mode=dmath}
}
\frac{1}{2}
\end{tblr}

\end{document}

Answer 2

well if I understood you question well, you're seeking to produce a table with math expressions, I would do that using array environment instead of tabular (you don't want to use $ in every cell, don't you :D), speaking of \dfrac and \frac, well the nccmath package provide medium size fractions which is \mfrac, let's give what we've said a shot, and let's create a small integration table (I'm not trying to remind you of calc II don't worry) :

\documentclass{article}
\usepackage{amssymb, nccmath}
\usepackage{makecell}

    \begin{document}
        \[
    \setcellgapes{5pt}
    \makegapedcells
    \begin{array}{|c|c|c|}
    \hline
    \makecell[l]{\mathbb{R}_+^*}  & x^n  & \mfrac{x^{n+1}}{n+1}+c \\
    \hline
    \mathbb{R}^*    & \mfrac{1}{x} & \ln \vert x\vert +c \\
    \hline
    \mathbb{R}      & e^{\lambda x} & \mfrac{1}{\lambda}e^x+c \\
    \hline
    \mathbb{R}      & \cos(\omega x)  & \mfrac{1}{\omega}\sin(\omega x)+c \\
    \hline
    \mathbb{R}      & \sin(\omega x)  & \mfrac{1}{\omega} \cos(\omega x)+c \\
    \hline
    \end{array}
        \]
    \end{document}

Here's the compilation result :

The code is pretty simple, for more vertical space around cells content you would employ \setcellgapes defined in the makecell package, there's also a problem of alignment in the first cell, so adding \makecell[l]{} will fix the problem.

Anyways I hope this will help you, this is how I usually make tables when all the cells contains mathematical expressions.