"L'Hôpital's rule" vs. "L'Hospital's rule"?
There was a change in French orthography in the mid 18th century, where some mute s's were dropped and replaced by the circumflex accent. In the Marquis's own time (1661-1704), his name was spelled "l'Hospital".
EDIT: Apparently in at least one letter the Marquis spelled his name "Lhospital". The 1716 edition of "Analyse des infiniment petits" at http://archive.org/texts/flipbook/flippy.php?id=infinimentpetits1716lhos00uoft has "l'Hospital". The 1768 edition of the book at http://archive.org/stream/analysedesinfini00lhos#page/n13/mode/2up has "l'Hôpital".