Differential (infinitesimal)

Differential or infinitesimal refers to a very small change or difference in a value. Imagine you have two numbers, 5 and 6. The difference between them is 1. Now imagine you have two very close numbers, like 5 and 5.1. The difference between them is very small or infinitesimal.

In math, we use differentials to help us understand how something changes in a very small way. For example, if we have a function like y = x^2, we can find out how much y changes when x changes just a little bit. We can do this by finding the derivative of the function.

The derivative is like a formula that tells us the rate of change or the slope of the function at any point. It helps us understand how the function changes when we make very small changes to the input value, x. We call this change dx, which is an infinitesimal difference. The derivative is denoted as dy/dx where dy is the differential or the change in y for a given change in x.

So, to explain it simply, differential or infinitesimal refers to a very small change in a value that we use in math to understand how things change in a very small way. It helps us calculate the slope or rate of change of a function at any point.