  In this paper, we study the estimation of the derivative of a regression
function in a standard univariate regression model. The estimators are defined
either by derivating nonparametric least-squares estimators of the regression
function or by estimating the projection of the derivative. We prove two simple
risk bounds allowing to compare our estimators. More elaborate bounds under a
stability assumption are then provided. Bases and spaces on which we can
illustrate our assumptions and first results are both of compact or non compact
type, and we discuss the rates reached by our estimators. They turn out to be
optimal in the compact case. Lastly, we propose a model selection procedure and
prove the associated risk bound. To consider bases with a non compact support
makes the problem difficult.
