Keðjureglan

Keðjureglan is a fundamental rule in differential calculus that describes how to calculate the derivative of a composite function. A composite function is one that is formed by applying one function to the result of another function. For example, if you have two functions, f and g, the composite function is written as f(g(x)).

The chain rule states that the derivative of f(g(x)) with respect to x is the derivative of the outer function f evaluated at the inner function g(x), multiplied by the derivative of the inner function g(x) with respect to x. In mathematical notation, if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx.

This rule is extremely useful because many complex functions can be broken down into simpler, nested functions. By applying the chain rule iteratively, one can find the derivative of even very complicated expressions. It is a cornerstone of calculus and is used extensively in various fields of science, engineering, and economics. Understanding and applying the chain rule is essential for mastering differentiation.