Generalizations of the derivative

A derivative is a way of finding out how quickly something is changing. Generalizations of the derivative are different ways of measuring how quickly something is changing, with specific methods to help figure out the answer. One way of generalizing the derivative is to look at higher-dimensional systems, or when there is more than one variable in the equation. In this case, the derivative is generalized to become a mathematical tool called the derivative matrix. This tool can help us measure how quickly something is changing in more than one direction. Another way of generalizing the derivative is to look at how things change over time. This type of problem is called a differential equation, and it is solved with a tool called the integral, which is similar to the derivative, but it can measure how something changes over time.