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Differentiation refers to the process of finding the derivative of a function. The derivative of a function at a specific point represents the instantaneous rate of change of the function at that point, or the slope of the tangent line to the function's graph at that point. This concept is fundamental in calculus and has wide-ranging applications in various fields of science, engineering, and economics.

There are several methods for differentiation. For elementary functions, rules such as the power rule, product rule, quotient rule, and chain rule are commonly employed. For instance, the power rule states that the derivative of x^n with respect to x is nx^(n-1). The chain rule is used to differentiate composite functions, which are functions within functions.

More complex differentiation techniques exist for advanced scenarios. Implicit differentiation is used when a function is not explicitly defined in terms of one variable, like y as a function of x. Parametric differentiation is applied when both x and y are defined as functions of a third variable, often denoted as t.

The geometric interpretation of differentiation is the slope of the tangent line. As the interval over which the change is measured approaches zero, the secant line through two points on the curve approaches the tangent line at a single point. The value of the derivative at that point is the slope of this tangent line. Differentiation is a cornerstone of understanding motion, optimization problems, and the behavior of systems that change over time.