the.com/chain rule
Differentiate the outside, then the inside tattles on itself too.
means A calculus rule for differentiating composite functions: the derivative of a function made of nested functions is the product of the derivatives of each layer, outer times inner.
from The term is a straightforward 19th/20th-century mathematical coinage, not a dramatic borrowing — it names the method itself, since differentiating nested functions means working link by link down a 'chain' of dependencies, multiplying derivatives as you go from outside in. The name describes the mechanism rather than echoing any older word.
- what it solves
- derivatives of functions stuffed inside functions
- core move
- multiply the outer slope by the inner slope
- secretly everywhere
- backpropagation in neural nets is just this
- common slip
- forgetting the inner derivative, not the outer