Hochschild (co)-homology of a formal quantization of an associative algebra

Question

Let $A$ be a commutative associative $k$-algebra and let $A[[\hbar]]$ be the formal deformation of $A$. I would like to know if there is a relation between the Hochschild co-homologies $HH^{\bullet}(A,A)$ and $HH^{\bullet}(A[[\hbar]],A[[\hbar]])$, respectively. In particular, is it true that $HH^{\bullet}(A[[\hbar]],A[[\hbar]])=HH^{\bullet}(A,A)[[\hbar]]$?