Chain rule
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: If
z is a function of a variable
y, which is itself a function of
x (see dependent variable), then
z is also a function of
x and the chain rule may be written In integration, the counterpart to the chain rule is the substitution rule.