A subscript that is closer to the tip of the nabla symbol

Question

With the command \nabla_x f(x, y), I have

I think this is not aesthetic. Is there a way to get the subscript closer to the tip of nabla symbol? Something looks like

Thank you so much for your elaboration!

Answer 1

Define a new command that nudges in the subscript (when present).

\documentclass{article}
\usepackage{amsmath}
\NewDocumentCommand{\Nabla}{e{^}}{%
  \nabla
  \IfValueT{#1}{{!#1}}%
  \IfValueT{#2}{^{#2}}%
}
\begin{document}
[
\Nabla_{x} f(x,y)
]
[
\Nabla f\quad \Nabla^{2} f \quad \Nabla^{2}_{x} f
]
\end{document}

Answer 2

Simply using \! a negative space.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
[
\boldsymbol{\nabla}_{!x}^{2} f(x, y)
]
\end{document}