[?] Avoid problem in integration with a DiracDelta?

Questions
1

I don’t see why these two equations should be different, but they return different values.

Integrate[Sin(2x)*D[DiracDelta(3x),x],{x,-1,1}] = -2/3
Integrate[Sin(2x)*DiracDelta'(3x),{x,-1,1}] = -2/9

When I do the problem by hand I find that the second answer of -2/9 to be the correct one. Am I misunderstanding the notation of D and ’ or is this a bug?

2

The issue is that:

D[f[3 x], x]

(*3 f'[3 x]*)

and:

f'[3 x]

(*f'[3 x]*)

are not the same thing.