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Let $E(\\tau)\\subseteq S_0(\\tau)$ be a symmetric operator space (on $\\mathcal{M}$) and let $\\mathcal{E}$ be a symmetrically-normed Banach ideal of $\\tau$-compact operators in $\\mathcal{M}$. We study (i) derivations $\\delta$ on $\\mathcal{M}$ with the range in $E(\\tau)$ and (ii) derivations on the Banach algebra $\\mathcal{E}$. 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