Differential Calculus

Differential calculus is a branch of mathematics focused on how things change. It studies rates of change and slopes of curves by using the concept of derivatives. A derivative measures how a function value changes as its input changes, effectively capturing the idea of instantaneous speed or acceleration. In practical terms, differential calculus helps us understand and predict behaviors in various fields, such as physics, engineering, and economics, by analyzing how quantities change in relation to one another. It provides the tools to optimize functions, finding maximum or minimum values, which is crucial in decision-making processes.