What is the chain rule?

The chain rule is a technique used when differentiating. It is needed when differentiating composite functions, i.e. when y = f(g(x)).For example, y = sin(x^3) is a composite function, where (referring to the general formula above) f(x) = sin(x), g(x) = x^3.The general form of the chain rule is dy/dx = g'(x) x f'(g(x)), i.e. you differentiate the inside function then multiply it by the differential of the whole function.Using the example from above: y = sin(x^3) dy/dx = 3x^2 x cos(x^3)Reverse chain rule can be used to quickly integrate a function if it is spotted.For example, if you were given the function y = 3x^2 x cos(x^3) to integrate, you may just integrate by parts or you may spot that it will be sin(x^3), by reverse chain rule.