The calculus rule for differentiating a composition of multivariable functions: how a partial derivative of an outer function with respect to a deep input is obtained by multiplying the partial derivatives along each path of the dependency chain, and summing over paths when an intermediate variable feeds several downstream quantities. Covers partial derivatives of functions of several variables, the tree/graph reading of variable dependencies, and why the multiplicative composition telescopes across an arbitrarily long chain. Purely mathematical -- stated for general composite functions, with no reference to neural networks, weights, or loss functions.
The core principle taught is the Multivariable Chain Rule, a fundamental theorem in multivariate calculus relating rates of change within composite functions. Formally defined through tree diagrams t…