  Let f be a modular form of weight k and Nebentypus $\psi$. By generalizing a
construction of Dabrowski and Delbourgo, we construct a p-adic L-function
interpolating the special values of the L-function
$L(s,\mathrm{Sym}^2(f)\otimes \xi)$, where $\xi$ is a Dirichlet character. When
s=k-1 and $\xi=\psi^{-1}$, this p-adic L-function vanishes due to the presence
of a so-called trivial zero. We give a formula for the derivative at s=k-1 of
this p-adic L-function when the form f is Steinberg at p. If the weight of f is
even, the conductor is even and squarefree, and the Nebentypus is trivial this
formula implies a conjecture of Benois.
