The reaction rate of a chemical reaction is a derivative. The derivative of the momentum of a body with respect to time equals the force applied to the body rearranging this derivative statement leads to the famous F = m a equation associated with Newton's second law of motion. In physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of the velocity with respect to time is acceleration. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point.ĭifferential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration.ĭifferentiation has applications in nearly all quantitative disciplines. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. The process of finding a derivative is called differentiation. The derivative of a function at a chosen input value describes the rate of change of the function near that input value.
The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. It is one of the two traditional divisions of calculus, the other being integral calculus-the study of the area beneath a curve. In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change.
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