derivations on the matrix semirings of max-plus algebra

Let $(s,oplus,otimes)$ be a matrix semiring of max-plus algebra with the addition operation $oplus$ and the multiplication operation $otimes$, where the set ( s ) consists of matrices constructed from real numbers together with the element negative infinity. a derivation on the semiring (s) is an additive mapping (delta) from (s) to itself that satisfies the axiom (delta(x otimes y) = (delta(x) otimes y) oplus (x otimes delta(y))), for every (x, y in s). from $s$ we construct all of semiring derivations of $s$ are denoted by $d$. on the set $d$, we defined two binary operations, i.e., addition &$dotplus$& and composition &$circ$&. we want to investigate the structure of $d$ over &$dotplus$& and &$circ$& operations. we show that ( d ) is not a semiring, but there exists a sub-semiring ( h ) (subseteq) ( d ). here, triple $(h,oplus,circ)$ is a semiring which is constructed from max-plus algebra.