Let $${L_1}$$ and $${L_2}$$ be two finite dimensional Lie algebras on arbitrary field F with no common direct factor and $$L = {L_1} \oplus {L_2}$$. In this article, we express the structure and dimension of derivation algebra of $$L$$, $$Der(L)$$, and some of their subalgebras in terms of $$Der({L_1})$$, $$Der({L_2})$$, $$Hom({L_1},Z({L_2}))$$, and $$Hom({L_2},Z({L_1}))$$.