m (mass) is a constant here, so it can be taken out (the product rule at work here!)

Therefore, F = m*(dv/dt) = ma (because acceleration a = dv/dt), which is basically Newton's Second Law defining force as the product of mass and acceleration.

Just a note:

Newton's Second Law (as Newton himself expressed it) = F = dp/dt = d(m*v)/dt

F = ma is Euler's formulation of Newton's second Law