How to understand the instantaneous change rate of point derivative? When the increment of the independent variable approaches the limit of 0, that is, the instantaneous rate of change of the point derivative of the point, the problem is why the increment of the independent variable is still meaningful when it is all 0, and why there is still a rate of change when there is no change at the point?

How to understand the instantaneous change rate of point derivative? When the increment of the independent variable approaches the limit of 0, that is, the instantaneous rate of change of the point derivative of the point, the problem is why the increment of the independent variable is still meaningful when it is all 0, and why there is still a rate of change when there is no change at the point?

The relationship between instantaneous rate of change and change. For example, when an athlete is ready to start at the starting line, although he doesn't move, the change is 0; but everyone's starting speed is different, that is, the rate of change varies from big to small. In fact, the rate of change has nothing to do with the change. When calculating the rate of change, only the amount of change is used