Yes, that is correct. You could also have used the quotient rule, which would give the same result a little more quickly.
Here's the quotient rule:
View attachment 30245
Multiplication is commutative i.e a*b=b*aView attachment 30246
comparing this with your final answer. It means that the arrangement:
Either (6q+2)sin(q) or sin(q) (6q+2) does not matter?