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In this paper, we study the automatic continuity in associative and nonassociative context of closable partially defined derivations on some Banach algebras whose domain not closed subalgebra. Precisely, we prove that if d is a derivation on a nonassociative Banach algebra A with zero annihilator such that every partially defined derivation on BL(A) is closable, then d is continuous. Also, we improve a result due to Villena asserted that every closable derivation defined on any nonzero ideal ofdoi:10.12988/ijma.2014.44104 fatcat:fybv7ckvvbeu7plzlirmok3oey