AI engineering glossary · Calculus optimisation
What is chain rule?
Chain rule: The rule for differentiating a function built from other functions: the derivative of f(g(x)) is f'(g(x)) * g'(x). Slopes of the inner and outer steps multiply. It is the mathematical engine of backpropagation, where gradients flow through many stacked layers.
Chain rule: an example
For y = (3x + 1)^2, let u = 3x + 1; then dy/dx = 2u * 3 = 6(3x + 1). At x = 1 the slope is 24.
Related terms
More Calculus optimisation terms
- Computational graph
- Condition number
- Conjugate gradient method
- Constrained optimisation
- Constraint
- Continuity
- Convergence
- Convergence rate
Where you learn it
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.