Let $(A,d)$ be a differential graded commutative and associative algebra. A derivation on $A$ is a linear endomorphism $L: A \to A$, that satsfies $L(ab)= L(a)b+ aL(b)$. More general a derivation of degree $n$ is a linear map $L: A \to A[n]$, (where $(A[n])_k:=A_{k+n}$) such that $L(ab)= L(a)b + (-1)^{n|a|}aL(b)$.
The graded vector space $Der(A)$ of all derivations (of any degree $n$), i.e $\oplus_n Der(A)_n$ with $Der(A)_n:=\{L:A \to A[n]\;|\;L\;linear\;and\;L(a)b + (-1)^{n|a|}aL(b)\}$ has itself a differential $d_{Der}$ defined by the equation $d_{Der}L=L\circ d \pm d\circ L$ (I'm not sure about the sign right now)
To summerize, we have two chain complexes $(A,d)$ and $(Der(A),d_{Der})$ and the question is:
Is there any relation between the homology $H(A)$ and the homology $H(Der(A))$?