Let $ R $ be a commutative ring. Let $ (X,\mathscr O_X) $ be a ringed space over $ R $, that is, let $ X $ be a topological space and let $ \mathscr O_X $ be a sheaf of $ R $-algebras on $ X $.
A derivation on $ X $ is a morphism $ D\colon \mathscr O_X\to \mathscr O_X $ of sheaves such that $$ \begin{aligned} D_U(\alpha f + \beta g) &= \alpha D_U(f) + \beta D_U(g)\\ D_U(fg) &= gD_U(f) + fD_U(g) \end{aligned} $$ for any open subset $ U\subset X $, $ \alpha,\beta\in R $ and $ f,g\in \mathscr O_X(U) $.
Define a presheaf $ \mathrm{Der}_{X} $ on $ X $ by $$ \mathrm{Der}_X(U) = \left\{\text{all the derivations $ D\colon \mathscr O_X{\restriction_U}\to \mathscr O_X{\restriction_U} $}\right\} $$ for any $ U\subset X $ open, where the restriction maps are the obvious ones and where $ \mathscr O_X{\restriction_U} $ is the obvious restriction of the structure sheaf of $ X $.
I'm trying to show that this guy is a sheaf. But I'm stuck.