According to the image point, the formula v=s/t can only calculate the average speed in a certain period of time, but not the instantaneous speed at a certain moment. If the speed keeps changing, how can we calculate the instantaneous speed at each moment? We can take an infinitesimal time period dt, during which the displacement of motion is ds, and divide them to get the instantaneous speed at a certain moment. As long as middle school physics solves the average quantity of a process or the instantaneous quantity of a uniform process, these quantities can be solved by elementary methods. But in college, you need the instantaneous quantity at a certain moment, so you must use the idea of differentiation. You can use Baidu Encyclopedia yourself.
To be more professional, we should talk about the difference between elementary mathematics and advanced mathematics. The main difference between them is the concepts of continuity and limit. Advanced mathematics is based on the definitions of continuity and limit.