Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules

For a Drinfeld module ρ defined over a separable closure of the rational function field, we determine all algebraic relations among its periods, quasi-periods, logarithms and quasi-logarithms. In particular, for periods and logarithms of ρ that are linearly independent over the endomorphism ring of ρ, we prove the algebraic independence of their hyperderivatives and the hyperderivatives of the corresponding quasi-periods and quasi-logarithms.