Relative Motion

Supposing an axes system is moving with respect to other axes system, what is the relationship between velocity in two system?

X-Y is a fixed reference frame and x-y is a moving reference frame. To begin with, consider the x-y axes only translate with respect to X-Y, but do not rotate. If A is any particle. The position vector of A as measured relative to the frame x-y is , where subscript A/B means "A relative to B" or "A with respect to B". The position of A with respect to X-Y,