AI engineering glossary · Calculus optimisation
What is multivariable chain rule?
Multivariable chain rule: The extension of the chain rule to functions of several variables: the derivative of an output with respect to an input is the sum, over every path connecting them, of the products of local partial derivatives along that path. It is how gradients are summed when a value feeds several later computations.
Multivariable chain rule: an example
If z = x*y with x = a + b and y = a * b, then dz/da = y*1 + x*b, adding one term per path from a to z.
Related terms
More Calculus optimisation terms
- Natural logarithm
- Nesterov momentum
- Newton's method
- Numerical differentiation
- Objective function
- Optimisation problem
- Partial derivative
- Power rule
Where you learn it
Multivariable chain rule is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.