Video Summary

A derivative is a measure of how a function changes as its input changes. It is defined as the limit of the ratio of the change in the output of the function to the change in its input as the input approaches a particular value. For example, if the function f(x) gives the position of a moving object at time x, then the derivative of f(x) at a particular time t is the instantaneous velocity of the object at that time. The derivative of a function can be calculated using the limit definition, or by using the product rule, quotient rule, or chain rule. The derivative is a powerful tool in mathematics, and it is used in a variety of fields, such as physics, engineering, and economics.