If we have a graded algebra $A$, and $D$ is a homogeneous linear map of grade $d = |D|$ on $A$ then $D$ is a homogeneous derivation if $$D(ab)=D(a)b+\epsilon^{|a||D|}aD(b)$$ $\epsilon\in\{-1,1\}$ acting on homogeneous elements of $A$. A graded derivation is sum of homogeneous derivations with the same $\epsilon$. If the commutator factor $\epsilon = 1$, this definition reduces to the usual case. If $\epsilon = -1$, however, then $D(ab)=D(a)b+(-1)^{|a|}aD(b)$, for odd $|D|$. They are called anti-derivations. Examples of anti-derivations include the [[exterior derivative]] and the [[interior product]] acting on [[differential form]]s.