  In this paper, we study the generalized differentiability of the metric
projection operator onto the positive cone in Hilbert spaces. We first
establish the formula for exactly computing the regular coderivative and the
Mordukhovich coderivative of the metric projection operator onto the positive
cone in Euclidean spaces. Then, these results are also established for the
projection operator onto the positive cone in the real Hilbert space $l_2$.
