In calculus, the chain rule is a formula for finding the derivative of function that is the composition of two or more functions (see function composition). The chain rule says that if we have a function h composed of differentiable functions g and f such that , then the derivative of h is calculated thusly:
For the above example where h is the composition of two functions, the chain rule tells us to first take the derivative of the “outer” function g, leaving the “inner” function f alone, and multiply that result by the derivative of the “inner” function f.
If we assign f(x) to the variable y, such that and assign h(x) to the variable z, such that , then z becomes a function of x by way of y, and we can write the chain rule in Leibniz’s notation:
« Back to Glossary Index