Why is the derivative of x^2 equal to 2x?

Differentiation is finding the slope of a graph; how steep it is at some point. In this case, we want to find out how steep the graph of x^2 is. To do this, we could look at the slope between two points on the line, and then move these points closer and closer, with the line between them getting closer and closer to the true slope of the curve. When we do this algebraically, we can find the slope of the line between the points with x-coordinates x and x+h. This is the change in y divided by the change in x, which is ((x+h)^2-x^2)/h. After some work, this is equal to 2x+h, which gets closer and closer to 2x as h gets closer to 0, which is the slope of the curve, or the derivative.