The chain rule is a rule in calculus for computing the derivative of a composite function. Given two differentiable functions f and g, the derivative of f∘g is (f∘g)\'(x) = f\'(g(x)) · g\'(x). The rule is parameterized by the outer function, the inner function, and the composition point, and it persists through mathematical notation, textbook teaching, and computational practice. It enables differentiation of nested functions — the mechanism by which compound expressions are untangled into tractable pieces — and is fundamental to both analytical and numerical computation across the physical sciences.
[formal: catena | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]