Differential calculus on ${\mathbb{Z}}_2^n$-supermanifolds

The concept of $\text{Zn}$-supermanifold has been recently proposed as a natural generalization of classical ($\text{Zs}$-graded) supergeometry, allowing for more complicated commutativity constraints. Here we continue the study of $\text{Zn}$-supergeometry by developing the foundations of differential calculus on $\text{Zn}$-supermanifolds.