Guillaume François Antoine, the Marquis de l’Hôpital, wrote the first differential calculus textbook, which he published in 1696. Leibniz’ calculus, which the Marquis had learned from Johann Bernoulli, was at this time a calculus of algebraic functions only. Nevertheless, by combining the techniques of the new calculus with methods of Euclidean geometry, Leibniz and the Bernoullis were able to investigate the properties of wide a variety of transcendental curves, including the cycloid, the quadratrix, and various spirals. Through his groundbreaking textbook, the Marquis de l’Hôpital shared these new methods with the French mathematical community. In this talk, I will describe l’Hôpital’s calculus, providing a variety of examples drawn from my forthcoming translation of Analyse des infiniment petits, a joint project with Sal Petrilli and Ed Sandifer.