Relative error ϵ in the first derivative of linear functions calculated in 2D as a function of the smoothing length. Upper rows depict the value of ϵ for ρ(x,y) = (1 + x) g cm^-3 obtained using the Gaussian (left) and the cubic spline (right) kernels. Bottom rows are the same but for the function  g cm^-3. Error profiles with crosses are for the direct derivative estimation.