Eventually, the options any LaTeX beginner desired were born!
The new (May 2021) package tabularray has two options to set the space before and after the table rows: abovesep and belowsep of the parameter rows!
The same package have also analogous options for columns, together with many other useful parameters and column types.
The environment tblr works both on math and text mode.
Thanks to Jianrui Lyu (the author)!
\documentclass{book}
\usepackage{tabularray}
\begin{document}
A pure \texttt{tblr} it's already OK
[
\begin{tblr}{c c}
f^{(n)}(x) & f^{(n)}(0) \
-2xe^{-x^{x^{x^2}}} & 0
\end{tblr}
]
but you can even set the space you need:
[
\begin{tblr}{cells={c},rows = {abovesep=6pt,belowsep=8pt},}
f^{(n)}(x) & f^{(n)}(0) \
-2xe^{-x^{x^{x^2}}} & 0
\end{tblr}
]
You can set the spacing also for one row only, indicating the number of the row with \verb|row{<number>}|:
[
\begin{tblr}{cells={c},row{2}= {abovesep=4pt},}
f^{(n)}(x) & f^{(n)}(0) \
-2xe^{-x^{x^{x^2}}} & 0
\end{tblr}
]
Here I add \verb|hline|s to better show the spacing:
[
\begin{tblr}{c c}
\hline
f^{(n)}(x) & f^{(n)}(0) \
\hline
-2xe^{-x^{x^{x^2}}} & 0 \
\hline
\end{tblr}
]
[
\begin{tblr}{cells={c},rows = {abovesep=6pt,belowsep=8pt},}
\hline
f^{(n)}(x) & f^{(n)}(0) \
\hline
-2xe^{-x^{x^{x^2}}} & 0 \
\hline
\end{tblr}
]
[
\begin{tblr}{cells={c},row{2}= {abovesep=4pt},}
\hline
f^{(n)}(x) & f^{(n)}(0) \
\hline
-2xe^{-x^{x^{x^2}}} & 0 \
\hline
\end{tblr}
]
\end{document}

\renewcommand{\arraystretch}{2}will stretch those too. To not effect the matrices, use\\[1em]to mark the row end within the table instead. – user3613932 Jun 10 '21 at 17:19{...}or\bgroup...\egroupor\begingroup...\endgroup. – Werner Jun 10 '21 at 17:24