Time dependence of operators in QM

I have a question.
I have seen Heisenberg’s equation of motion for observables:
$$frac{dA}{dt}=frac{1}{ihbar}[A,H]+frac{partial A}{partial t}.$$
However if I want to calculate for example the mean time dependence of an operator in the Schrödinger picture then I arrive at the following:
$langle A(t)rangle=langle psi|e^{iHt/hbar}Ae^{-iHt/hbar}|psirangle$ One can then use the Baker Hausdorff identity to calculate the time dependence of the operator. My question is this the solution to the Heisenberg’s equation of motion?