En cálculo, la regla de la cadena es una fórmula para la derivada de la composición de dos funciones. Tiene aplicaciones en el cálculo algebraico de derivadas cuando existe composición de funciones.

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In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions. That is, if f and g are functions, then the chain rule expresses the derivative of their composition f ∘ g (the function which maps x to f(g(x)) in terms of the derivatives of f and g and the product of functions as follows: This can be written more explicitly in terms of the variable. Let F = f ∘ g, or equivalently, F(x) = f(g(x)) for all x. Then one can also write The chain rule may be written, in Leibniz's notation, in the following way. We consider z to be a function of the variable y, which is itself a function of x (y and z are therefore dependent variables), and so, z becomes a function of x as well: In integration, the counterpart to the chain rule is the substitution rule.

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