Differential $\Gamma$ -(semi)hyperrings are $\Gamma$ -(semi)hyperrings equipped with derivation, which is a linear unary function satisfying
the Leibniz product rule.We introduce the notions of derivation and weak derivation on $\Gamma$ -hyperrings and $\Gamma$ -semihyperrings
and obtain some important results relating to them in a specific way.
