Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{infty}$ norms.