In this article, our aim is to estimate the successive derivatives of the stationary
density f of a strictly stationary and β-mixing process (Xt)t≥0. This process is observed at discrete times
t = 0,Δ,...,nΔ. The
sampling interval Δ can be fixed or small. We use a penalized
least-square approach to compute adaptive estimators. If the derivative
f(j) belongs to the Besov space \hbox{$\rond{B}_{2,\infty}^{\alpha}$}, then our estimator converges at rate (nΔ)−α/(2α+2j+1). Then we consider a diffusion with known diffusion
coefficient. We use the particular form of the stationary density to compute an adaptive
estimator of its first derivative f′. When the sampling interval
Δ tends to 0, and when the diffusion coefficient is known, the
convergence rate of our estimator is (nΔ)−α/(2α+1). When the diffusion coefficient is known, we also
construct a quotient estimator of the drift for low-frequency data.