This note describes a possible approach to the direct calculation of both derivatives and integrals of power functions using rather simple algebra and limits that could be easily accessible to students beginning a calculus course. The calculations provide a powerful example of the fundamental theorem, and could be used to allow students to discover the fundamental theorem from the example. The main calculation, which is not found in many calculus textbooks and is due to Descartes, is described by Maor [2]. While this approach may seem like the popular American ‘reform’ calculus, one may find a somewhat similar approach (presenting integral calculus from first principles) in Tom Apostol’s classic and lovely text [1].