Past exam of the physics A course of the University of Cambridge / 2011 / Paper 2 / Section A / 3

The canonical commutation relation is $[p_x,x]=-i\hslash I$. Applying the commutator product rule on a common operator domain,Equivalently, applying both sides to a twice differentiable test function gives $-{\hslash }^2[(xf{)}^{\prime \prime }-x{f}^{\prime \prime }]=-2{\hslash }^2{f}^{\prime }$, the same result.