Guillaume François Antoine de l’Hôpital’s Analyse des infiniment petits (1696) was the first ever calculus textbook. It was also something of an enigma. For one thing, it was published anonymously, although de L’Hôpital’s authorship was no secret. Also, it made no mention of the integral calculus: instead, its introduction to the differential calculus was followed by what can only be described as an advanced text on differential geometry, motivated by what were then cutting-edge problems in mechanics and optics. However, the oddest aspect of this book is its genesis. The introductory chapters were based on Johann Bernoulli’s Lectiones de calculo differentialium, lessons that only ever existed in manuscript form and were unknown to the scholarly community until 1921. De l’Hôpital received his copy when he hired Bernoulli to tutor him in 1691-1692. Subsequently, he “purchased” the advanced material of the later chapters, in an arrangement under which he supported Bernoulli with a stipend in 1694-1695. In this talk, we will consider both the mathematics that was presented in the Analyse and the process by which it came into being. We will compare de l’Hôpital’s exposition of the elements of the differential calculus with that of Bernoulli and examine some of the more advanced results presented in the Analyse.