Consider a multivalued mapping \(F:X\to Y\) between Banach spaces, and a point \((x,y)\) in its graph. Let \(X^*\) and \(Y^*\) denote the topological duals of \(X\) and \(Y\), respectively. Roughly speaking, the co-derivative of \(F\) at \((x,y)\) is a multivalued mapping \(D^*F(x,y): Y^*\to X^*\) that describes the first-order behavior of \(F\) around the point \((x,y)\). This paper explores some calculus rules for this mathematical object, special attention being paid to the composition and the addition of multivalued mappings. For a related reference, see \textit{B. S. Mordukhovich} [Nonlinear Anal., Theory Methods Appl. 30, No. 5, 3059-3070 (1997; preceding review)].