The Tutte polynomial of a morphism of matroids - 5. Derivatives as generating functions of Tutte activities

We show that in an ordered matroid the partial derivative ∂p+qt/∂xp∂yq of the Tutte polynomial is p!q! times the generating function of activities of subsets with corank p and nullity q. More generally, this property holds for the 3-variable Tutte polynomial of a matroid perspective.