rate of formation, vn,y or vc,y

Like the rate of consumption, the rate of formation of a specified product may be defined in two ways:

As the time derivative of the amount of a product. Thus for a product Y, present at any time in amount $n Y$ . the rate of its formation may be given by:
$v n Y = d n Y d t$
This definition is particularly appropriate for open systems.
For kinetics in closed systems it is more usual to define a rate of formation per unit volume, denoted $v c Y$ :
$v c Y = 1 V d n Y d t$
When the volume is constant this reduces to:
$v c Y = 1 V d n Y d t = d Y d t$
When the volume is not constant the relationship $n Y = Y V$ may be differentiated to give:
$d n Y = V d Y + Y d V$
and the rate of formation becomes:
$v c Y = d Y d t + Y V d V d t$
A rate of formation may be specified even for a reaction of time dependent stoichiometry or of unknown stoichiometry.

Source:

PAC, 1996, 68, 149 (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 181