Why do I get the same results from each of the first pair below, but different results from each of the second and third pairs below? How do I rewrite In[653] and In[655] to get the correct result?

    In[657]:= MellinConvolve[g[x], DiracDelta[x - 1], x, y]

    Out[657]= g[y]

    In[658]:= Assuming[y > 0, Integrate[g[x] DiracDelta[y/x - 1]/x, {x, 0, Infinity}]]

    Out[658]= g[y]

------------------------
In[652]:= MellinConvolve[g[x], DiracDelta'[x - 1], x, y]

Out[652]= g[y] + y Derivative[1][g][y]

In[653]:= Assuming[y > 0, Integrate[g[x] DiracDelta'[y/x - 1]/x, {x, 0, Infinity}]]

Out[653]= g[y] - y Derivative[1][g][y]

In[654]:= MellinConvolve[g[x], DiracDelta''[x - 1], x, y]

Out[654]= 2 g[y] + 4 y Derivative[1][g][y] + y^2 (g^\[Prime]\[Prime])[y]

In[655]:= Assuming[y > 0, 
Integrate[g[x] DiracDelta''[y/x - 1]/x, {x, 0, \[Infinity]}]]

Out[655]= 2 g[y] + y (-2 Derivative[1][g][y] + y (g^\[Prime]\[Prime])[y])

I'm using Mathematica 11 Home Edition running on Ubuntu LTS.

Version Number: 11.0.0.0

Platform: Linux x86 (64-bit)