Differential Calculus

Differential calculus is a branch of mathematics that focuses on the concept of the derivative, which quantifies how a function changes as its input changes. It studies rates of change, slopes of curves, and instantaneous velocities. By employing limits, differential calculus allows us to determine the behavior of functions at specific points, helping to identify maxima and minima. Key concepts include differentiation rules (such as product and chain rules), applications to tangent lines, optimization problems, and motion analysis. This field serves as a foundational tool in physics, engineering, and economics, enabling precise modeling of dynamic systems and change.