EN
Let k be a field of chracteristic p > 0. We describe all derivations of the polynomial algebra k[x,y], homogeneous with respect to a given weight vector, in particular all monomial derivations, with the ring of constants of the form $k[x^{p},y^{p},f]$, where $f ∈ k[x,y]∖ k[x^{p},y^{p}]$.