Since lne = 1, does d/dx of lne = 0

And if so, is this the logic:

d/dx lne = [1/e * d/dx (e)] = [1/e * 0] = 0

and/or

d/dx lne = d/dx log(base e)(e) = d/dx 1 = 0

are there any other ways to make the point that d/dx of lne = 0?

d/dx (constant) = 0

and ln(e) it's a constant number and not a variable