This notation is not so common in basic mathematics, but it is so incredibly convenient, especially with Einstein notation as shown at Section "Einstein notation for partial derivatives":

$∂_{0}F(x,y,z)=∂x∂F(x,y,z) ∂_{1}F(x,y,z)=∂y∂F(x,y,z) ∂_{2}F(x,y,z)=∂x∂F(x,y,z) $

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