Confused by Operator Algebra: Checking Intermediate Step

[BWV]

I get confused by the operator algebra - this is the commutator for q & p from wikipedia
Am I correct on the intermediate step I plugged in there?

because of the product rule you get as the intermediate step:

=d/dx x Ψ(x) + x d/dx Ψ(x) - x d/dx Ψ(x)

and d/dx x =1

so

 

[mathman]

Looks good.

 

[BWV]

Great, thanks for looking at it