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What is a Derivative?


A derivative in calculus is a measure of how a function changes as its input changes. In other words, it represents the rate of change or the slope of the function at a given point. Derivatives are a central concept in differential calculus and have numerous applications in various fields, such as physics, engineering, and economics.

Derivatives can be calculated using different methods, including the limit definition, the power rule, the product rule, the quotient rule, and the chain rule. Higher-order derivatives can also be computed, which represent the rate of change of the rate of change, and so on.

Derivatives can be used to solve problems related to optimization, such as finding the maximum or minimum values of a function. They also play a crucial role in solving differential equations, which are equations involving derivatives and are widely used to model real-world phenomena.

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