Abstract
Abstract “Derivatives” includes the definition of derivative, derivative rules, and some applications of the derivative, all from an infinitesimal perspective. The definition of derivative is derived by applying the slope formula to the point of tangency and a second point infinitely close to that point. A local linearity formula is presented early in the chapter and is the basis for calculation-style proofs of derivative rules, including a simple proof of the chain rule. All the customary derivative rules and formulas are presented, but note that this is not an “early transcendentals” text. The section on trig derivatives includes an approximation formula that simplifies the computation of many trigonometric limits. Applications include tangent lines, motion, and economics. Related rates are presented in two sections, first with Pythagorean relationships only and then for non-Pythagorean relationships, reducing the number of tasks a reader must learn concomitantly.
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