  In this paper, we prove strict Frechet differentiability of the metric
projection operator onto closed balls in Hilbert spaces and onto positive cones
in Euclidean spaces. We find the exact expressions for Frechet derivatives.
Since Frechet differentiability implies Gateaux directional differentiability,
the results obtained in this paper strengthen the results obtained in [8] and
[10] about the directional differentiability of the metric projection operator
onto closed balls in Hilbert spaces and positive cones in Euclidean spaces and
in the real Hilbert space l2.
