In 1696 the Marquis de L’Hospital (1661-1704) published the ‘Analyse des infiniment petits’ pour l’intelligence des lignes courbes, the first systematic work on differential calculus. The ‘Analyse’ played a fundamental role in the circulation and teaching of the Leibnizian calculus. To help readers understand the ‘Analyse’ three commentaries were subsequently published in France: i) ‘Éclaircissemens sur l’Analyse des infiniment petits’ (Paris, 1725), by Pierre Varignon (1654-1722); ii) ‘Commentaire sur l’Analyse des infiniment petits’ (Paris, 1721), by Jean Pierre Crousaz (1663-1750); iii) ‘Analyse des infiniment petits, suivie d’un nouveau commentaire pour l’intelligence des endroits les plus difficiles de cet ouvrage’ (Avignon, 1768), by Aimé Henri Paulian (1722-1802). The main aim of this contribution is to show how the authors of these commentaries interpreted and explained some fundamental concepts contained in the ‘Analyse’, such as the definition of difference and the rule of the product