Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $Vert hat{T}_n - T(f) Vert_2$ be the usual $L_2$ norm of the restriction of $hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $Vert hat{T}_n - T(f) Vert_2$ is discussed.