Differential (mathematics)

Imagine you are playing a game with your friend where you have a number and your friend has to guess what it is. Every time they make a guess, you tell them if their guess is too high or too low, and they use that information to make a better guess the next time.

Differential is kind of like that game, but with math. Instead of a number, you have a function (like y = 2x + 3), and instead of guessing, you want to know how the function is changing at a certain point. The way you find this out is by using something called a derivative, which is like the "too high/too low" information you give your friend.

The derivative tells you how much the function is changing at a specific point (think of it like how steep a hill is at a certain spot). If the derivative is positive, that means the function is increasing, and if it's negative, that means the function is decreasing.

So let's say you're trying to figure out how fast a car is going at a certain point in time. You could use differential to find the derivative of the car's position function, and that would tell you how much the car is moving at that exact moment.

Overall, differential is a way to find out how things are changing at specific points, kind of like giving your friend hints in a guessing game!