In existographies, Adrien-Marie Legendre (1752-1833) (IQ:175|#274) (Murray 4000:16|M) (GME:21) (Eells 100:11) (CR:3) was a French mathematician noted for his mathematical state function “transformation” procedure, known as the Legendre transform (or Legendre transformation), in which one specific variable of a state function equation can be converted into a more convenient form.

Partial differentials
In his 1786 “Memoir on how to Distinguish the Maxima and Minima in Calculus of Variations”, Legendre is said to have established the modern notation and use for the partial differential of the form: [1]

$\frac{\partial u}{\partial x} \,$

This partial differential logic was then adopted by German mathematician Carl Jacobi in 1841 after which it became the norm.

References
1. (a) Legendre, Adrien-Marie. (1786). “Memoir on how to Distinguish the Maxima and Minima in Calculus of Variations” (Memoire sur la manière de distinguer les maxima des minima dans le Calcul des Variations), in: Histoire de l'Academie Royale des Sciences, Annee M. DCCLXXXVI (quote, pg. 8), pp. 7-37, Paris, M. DCCXXXVIII (1788).
(b) Miller, Jeff. (2009). “Earliest Uses of Symbols of Calculus”, Jeff560.tripod.com.