The following problem says the rate of change of x with respect to t is 3 meters per second.

Now why should we interpret the red sentence as a derivadive(dx/dt)?And why (dy/dt) for the blue one?

Why not (Delta x/Delta t) or (Delta y/Delta t)?

Thanks.For 10-meter ladder is leaning against the wall of a building, and the base of the ladder is sliding away from the building at a rate of 3 meters per second. How fast is the top of the ladder sliding down the wall when the base of the ladder is 6 meters from the wall?