Let us say, you are buying 10 chocolates for 20 dollars. If you divide 20 by 10, you get 2. So 2 dollar is the price of 1 chocolate. Division always gives the rate. In this case cost per unit.
Another example: a car covers 120 km in 2 hours. 120/2 = 60 km, It is the speed of the car. Also rate of distance traveled by the car. (distance traveled in one hour)
In general Division y/x, gives the value of y when x is unity.
Now let us assume that, we have two series as follows.
x = 1,2,3,4,5,6....
y = 1,4,9,16,25,36... = x^2
Here, I want to find y/x. But the values are not uniform and they are growing. What to do? Here calculus comes to our help.
It says, if y=x^2, then y/x or more correctly dy/dx = 2x.
Let us verify,
x = 3; y = 9
x =4; y=16
For unit change in x(4-3=1), the change in y is 16 - 9 =7
The average of x = 3 and 4 is 3.5
So 2x=2*3.5 = 7
Hence, for unit change in x, the change in y is 2x - verified.
For functions like, y =x^3, y = log(x)
y=sin x and y = 3x+2x^2, the calculus gives us the division of dy/dx(differentiation) or the rate of change of y with respect to x.
Using calculus, we can calculate, velocity, acceleration, inflation, current, voltage etc for continuously varying quantities.