This concept covers linear approximation expressed in the language of differentials rather than derivative notation: for y = f(x), a small change dx in the input produces an approximate change dy = f′(x)dx in the output, so that f(x₀ + dx) ≈ y₀ + dy, providing an alternative but formally equivalent formulation of the tangent-line approximation. It relies on formal definitions of the differential dy of a function (computed via the same differentiation rules as the derivative, including the chain rule, but expressed with a trailing dx factor) and on selecting a base point where the function's value is known exactly, so that a nearby, harder-to-evaluate value can be estimated. This belongs to single-variable calculus, within the theory of linear (local) approximation, presenting differentials as a notational reformulation of the derivative-based tangent-line approximation method.
This concept covers linear approximation expressed in the language of differentials rather than derivative notation: for y = f(x), a small change dx in the input produces an approximate change dy = f…