derivative of `norm` at 0

norm is not differentiable at 0, so at best you can return a subgradient. It appears that the subgradient is 1.0 at 0.0 (and -1.0 at -0.0).

julia> ForwardDiff.gradient(norm, [0.0, 0.0])
2-element Array{Float64,1}:
 0.0
 1.0

julia> ForwardDiff.gradient(norm, [0.0, -0.0])
2-element Array{Float64,1}:
 -0.0
 -1.0

I'm wondering if it would be worth it to define Base.norm on ForwardDiff.Dual, and return a subgradient of 0.0 at both 0.0 and -0.0

Also perhaps I missed this, but I think it would be nice to mention somewhere that in generic auto-diffable code sqrt(sum(v.^2)) should be replaced with norm, since sqrt is singular at 0, and produces a NaN when composed with a function with 0 gradient (0*Inf = NaN).

Start by reproducing the ForwardDiff.gradient examples for norm at 0.0 and -0.0, then inspect the ForwardDiff.gradient path and the proposed Base.norm behavior for Dual values. Done means the zero cases have a deliberate subgradient behavior and the guidance about replacing sqrt(sum(v.^2)) with norm is addressed.