  In this paper, we study derivatives of powers of Euclidean norm. We prove
their H\"older continuity and establish explicit expressions for the
corresponding constants. We show that these constants are optimal for odd
derivatives and at most two times suboptimal for the even ones. In the
particular case of integer powers, when the H\"older continuity transforms into
the Lipschitz continuity, we improve this result and obtain the optimal
constants.
