One way to find dI would be from lnI/I=pi/2.Assuming pi/2 constant for time being, we get:

d(lnI/I)=0

dI/(I^3)-lnI/I^2=0

dI = IlnI = -(lnI)/I = ln (I^I)=-ln(I^(1/I)= -pi/2 so that if

-I= h(I^(1/I)), dI = -ln(I^(1/I)).

so we can have

-IdI = -W(- ln(I^(1/I)) = I*(Pi/2)

IdI= W(-ln(I^(1/I))= -I*(pi/2)

We can integrate dI , IdI , etc over all hyperdimensions or finite interval of and get some values. First impression is that pi is not a constant moving from one hyperdimension to next, otherwise we get non-identities, but this have to be little experimented with.

And so on. More later.

d(lnI/I)=0

dI/(I^3)-lnI/I^2=0

dI = IlnI = -(lnI)/I = ln (I^I)=-ln(I^(1/I)= -pi/2 so that if

-I= h(I^(1/I)), dI = -ln(I^(1/I)).

so we can have

-IdI = -W(- ln(I^(1/I)) = I*(Pi/2)

IdI= W(-ln(I^(1/I))= -I*(pi/2)

We can integrate dI , IdI , etc over all hyperdimensions or finite interval of and get some values. First impression is that pi is not a constant moving from one hyperdimension to next, otherwise we get non-identities, but this have to be little experimented with.

And so on. More later.