Verified answer

It's just a definition (except that you have a typo)

ma = m d^2 x / dt^2

v = dx/dt

a = dv/dt = d^2 x / dt^2

F = ma

But mass times acceleration is the rate of change of momentum

and that is

F=ma=dp/dt= d(mv)/dt

If mass is constant then

F=ma= dp/dt=d(mv)/dt = m dv/dt

and we know that v , velocity, is the rate of change of distance, x

so we get

F=ma= dp/dt=d(mv)/dt =m dv/dt = m d(dx/dt)/dt= m d²x/dt²

since the m is on both sides of the equation, just cancel it. then you just have the definition of acceleration, which is the second derivative of the position function, or the derivative of the velocity function.