differentiate

Differentiation is a fundamental concept in calculus, referring to the process of finding the rate at which a quantity changes with respect to another. It involves determining the derivative of a function, which represents the slope of the tangent to the function's graph at any given point. Developed independently by Isaac Newton and Gottfried Leibniz in the 17th century, differentiation is crucial in understanding how a small change in one variable affects another. For instance, if a function describes an object's position over time, its derivative gives the object's velocity. Beyond mathematics, "differentiate" generally means to identify or recognize differences between things or people. For example, in business, differentiating a product involves highlighting features that set it apart from competitors. This concept is vital in various fields, including physics, engineering, and economics, for modeling and analyzing dynamic systems. The inverse process of differentiation is integration, which aims to find the original function from its derivative.