On dimension of a special subalgebra of derivations of nilpotent Lie algebras

‎Let L be a Lie algebra‎, ‎Der(L) be the set of all derivations of L and Derc(L) denote the set of all derivations α∈Der(L) for which α(x)∈[x,L]:={[x,y]|y∈L} for all x∈L‎. ‎We obtain an upper bound for dimension of Derc(L) of the finite dimensional nilpotent Lie algebra L over algebraically closed fields‎. ‎Also‎, ‎we classify all finite dimensional nilpotent Lie algebras L over algebraically closed fields for which dimDerc(L) attains its maximum value.