  In this paper we consider the chain rule formula for compositions $x\mapsto
F(x, u(x))$ in the case when $u$ has a Sobolev or BV regularity and $F(x,z)$ is
separately Sobolev, or BV, with respect to $x$ and $C^1$ with respect to $z$.
Our results extend to this "nonautonomous" case the results known for
compositions $x\mapsto F(u(x))$.
