{title2=$\partial_0 F$}
{title2=$\partial_1 F$}

This notation is not so common in basic mathematics, but it is so incredibly convenient, especially with <Einstein notation> as shown at <einstein notation for partial derivatives>{full}:
$$
\partial_0 F(x, y, z) = \pdv{F(x, y, z)}{x} \\
\partial_1 F(x, y, z) = \pdv{F(x, y, z)}{y} \\
\partial_2 F(x, y, z) = \pdv{F(x, y, z)}{x} \\
$$

This notation is similar to <partial label partial derivative notation>, but it uses indices instead of labels such as $x$, $y$, etc.


 Partial index partial derivative notation