Suppose that y is the height of some plant, say a particular sunflower growing in a garden, and x is time.
I don't know the exact figures, so these are just any numbers, just to illustrate the idea.
So one could say, for example, in 20 days the sunflower has grown 40 inches.
So, one could say, ah, that is a rate of change of two inches per day.
However, the growth might have been more rapid on some days than on others, so 2 inches per day is an average, and on any particular day, the growth might be 2 inches, it could be more, it could be less, or it could be exactly 2 inches.
So if, say, we looked at the growth over some chosen 5 day period, the sunflower has grown 11 inches in thoise five days, so 2.2 inches per day on average during that time period.
Now, if we reduce the time period to, say. half a day, we might find that in that paeticular half day it has grown 1.5 inches, so that is an average of 3 inches per day.
On a different half a day, it may have grown 0.4 inches, so that is a average of 0.8 inches per day.
Now if we take the length of time over which we take the change of height down smaller and smaller, then the average is being found more frequently.
Now in the limit as that time gap for the sample tends to zero, that average growth rate over the tme period becomes more accurate as to what is happening at that instant.
That rate of change at that instant is what is designated by dy/dx in the mathematics.
William