The chain rule is a formula for finding the derivative of a composite function. It uses a variable depending on a second variable, , which in turn depend on a third variable, . The derivative of any function is the derivative of the function itself, as per the power rule, then the derivative of the inside of the function. and so on, for as many interwoven functions as there are. For a multivariable function of variables, the chain rule becomes the dot product of the gradient and the derivative of a vector function.