\vec F = \frac{\hbox{d}(m\cdot \vec v)}{\hbox{d}t} = m \frac{\hbox{d} \vec v}{\hbox{d}t} + \vec v \frac{\hbox{d}m}{\hbox{d}t} = m \frac{\hbox{d} \vec v}{\hbox{d}t}