What is differentation and how does it work?

Differentiation is how to find the gradient of a line. For example, the line y = 3x has a gradient of 3. Similarly, y = 4x + 2 has a gradient of 4. However, for most lines, the gradient isn't the same along the line in all places, such as y = x squared; the line has a different gradient at different points along the line. So, since we cannot find the gradient for the whole line at once, we instead have to find it for each point. Luckily, there is a simple rule for doing this for lines with powers in them; the gradient (ie differentating) simply needs to multiply by the power and take one from the power. So y = x squared has a gradient of 2x and y = x cubed add 4x squared has a gradient of 3x squared + 8x
The reason this works is because, when you think of the gradient, you take a point on a line and then a nearby point and find the change in y divided by the change in x. So, for the gradient at a point, all you need to do is to take closer and closer points until they are infinitesimally close.