This article explains how these four things fit together and shows some examples of what they are used for. Derivatives are the most fundamental concept in calculus. If you have a function, a derivative tells you how much that function changes at each point. If we start with the function , we can calculate the derivative as . Here are those two functions graphed. One use of derivatives is for optimization – also known as finding the lowest part on a graph. If you were at and wanted to know wh...