Differential operators are mathematical tools used to perform differentiation, which is the process of finding the rate at which a function changes. They are often represented using symbols like D, where D denotes the derivative with respect to a variable. For example, applying the operator D to a function f(x) gives the first derivative, f'(x). These operators can be combined and manipulated to create higher-order derivatives, such as the second derivative, represented as D^2. Differential operators are essential in various fields, including physics, engineering, and economics, as they help model dynamic systems and analyze changes in quantities.