  Let X be a Banach space over field F (R or C). Denote by B(X) the set of all
bounded linear operators on X and by F(X) the set of all finite rank operators
on X. A subalgebra A of B(X) is called a standard operator algebra if A contain
F(X). We give a brief proof of a well-known result that every derivation from A
into B(X) is inner. There is another classical result that every local
derivation on B(X) is a derivation. We extend the result by proving that every
local derivation from A into B(X) is a derivation. Based on these two results,
we prove that every 2-local derivation from A into B(X) is a derivation.
