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Power Rule

Definition

The power rule is a calculus rule used to find the derivative of a function that is raised to a constant power. It states that if f(x) = x^n, where n is a constant, then the derivative of f(x) with respect to x is equal to n*x^(n-1).

Analogy

Think of the power rule as an assembly line for derivatives. Just like an assembly line takes raw materials and transforms them into finished products, the power rule takes a function and transforms it into its derivative by reducing the exponent by 1 and multiplying it with the original coefficient.

Related terms

Exponential Function: A mathematical function in which an independent variable appears in one or more exponents. For example, f(x) = 2^x.

Chain Rule: A calculus rule used to find the derivative of composite functions. It allows us to differentiate functions within functions.

Derivative: The rate at which a function changes as its input variable changes. It represents the slope of the tangent line to the graph of a function at any given point.