Computing Differentials in Single-Variable Calculus
A differential expresses the linear approximation of a function's change via its derivative, notated as d(f) rather than df/dx, with the differentiation variable implicit rather than written explicitly. Differentials obey the same combination rules as derivatives — linearity (sum/constant multiple), the chain rule, and the product rule — but applied to the "d" operator rather than to d/dx. This belongs to single-variable calculus and formalizes the notion of an infinitesimal change, connecting derivative rules directly to differential notation used in related-rates and approximation contexts.
Computing Differentials in Single-Variable Calculus
A differential expresses the linear approximation of a function's change via its derivative, notated as d(f) rather than df/dx, with the differentiation variable implicit rather than written explicit…