Dérivée en s=1 de la fonction L p-adique du carré symétrique dʼune courbe elliptique sur un corps totalement réel

We prove a formula for the derivative of the p-adic L-function associated with the symmetric square representation of an elliptic curve over a totally real field in which p is inert, under certain assumptions on the conductor. In particular, this proves a conjecture of Greenberg on trivial zeros. The method is to generalize unpublished calculations of Greenberg and Tilouine.