one(::type(Dual))

Currently, one returns a Dual number. It seems like it could simply return the underlying value type instead. i.e. change these lines to

Base.one(d::Dual) = one(typeof(d))
Base.oneunit(d::Dual) = oneunit(typeof(d))
Base.one(::Type{Dual{T,V,N}}) where {T,V,N} = one(V)
Base.oneunit(::Type{Dual{T,V,N}}) where {T,V,N} = Dual{T}(oneunit(V), zero(Partials{N,V}))

which is still correct since one(V) is still a multiplicative identity for Dual, and type promotion takes care of the rest. In general, one(x) in Julia need not return the same type as x — if you want the same type, you use oneunit, which is why I added a method for Dual (since they otherwise fall back to calling one).

The advantage of this is that code that is designed to "strip the units" from numbers will then work with Dual numbers as well. For example, this code in QuadGK.jl will work, and you will suddenly be able to differentiate numerical integrals:

julia> ForwardDiff.derivative(x -> quadgk(y -> y^2, 0, x)[1], 4)
16.0

Start in src/dual.jl at the Base.one and Base.oneunit methods around lines 356-357. Check the linked QuadGK example and verify that differentiating the shown numerical integral works while the Dual identity behavior remains correct; the issue is done when those calls produce the expected derivative.