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Calculus, a fundamental branch of mathematics, studies continuous change. It provides a framework for understanding how quantities vary over time or in relation to other variables. Calculus heavily relies on the concepts of limits, derivatives, and integrals.

Derivatives delve into the rate of change of a function. The derivative, symbolized as dy/dx, represents the slope of a tangent line to a curve at a specific point. This slope quantifies how a function's output (y) changes with respect to its input (x). The process of finding the derivative is called differentiation.

The real-world applications of calculus are vast and diverse. In physics, derivatives model velocity and acceleration, enabling us to understand the motion of objects. Engineers harness the power of calculus to design efficient structures, predict material behavior, and simulate complex systems. Economists use derivatives to analyze marginal costs and revenues, optimizing production and pricing strategies.

The development of calculus is credited to two brilliant minds: Isaac Newton and Gottfried Wilhelm Leibniz. Their independent discoveries in the late 17th century revolutionized mathematics and paved the way for countless scientific and technological advancements.