The domain 𝒟 ( δ ) of a closed ∗ -derivation δ in C ( K ) ( K : a compact Hausdorff space) is a generalization of the space C ( 1 ) [ 0 , 1 ] of differentiable functions on [ 0 , 1 ] . In this paper, a problem proposed by Jarosz (1985) is studied in the context of derivations instead of C ( 1 ) [ 0 , 1 ] .