How can I auto differentiate the function `cd`

with respect to `p`

?

```
using ForwardDiff
using NLsolve
function cd(; p=[1.0, 1.0], i=100)
function sys(sto, x; p=p, i=i)
x1 = x[1]
x2 = x[2]
p1 = p[1]
p2 = p[2]
sto[1] = x1/p2 - x2/p1
sto[2] = i - p1*x1 - p2*x2
end
sol = nlsolve(sys, [1.0, 1.0], method=:trust_region, autodiff=:forward)
return sol.zero
end
```

I get an error:

```
julia> ForwardDiff.jacobian(p -> cd(; p=p), [1.0, 1.0])
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2})
Closest candidates are:
(::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat at rounding.jl:200
(::Type{T})(::T) where T<:Number at boot.jl:760
(::Type{T})(::AbstractChar) where T<:Union{AbstractChar, Number} at char.jl:50
...
Stacktrace:
[1] convert(#unused#::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2})
@ Base ./number.jl:7
[2] convert(#unused#::Type{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, d::ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}, 2})
@ ForwardDiff ~/.julia/packages/ForwardDiff/5gUap/src/dual.jl:378
[3] setindex!(A::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, x::ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}, 2}, i1::Int64)
@ Base ./array.jl:839
[4] (::var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"})(sto::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}; p::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, i::Int64)
@ Main ./REPL[4]:8
[5] (::var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"})(sto::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}})
@ Main ./REPL[4]:4
[6] vector_mode_dual_eval(f!::var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, y::Vector{Float64}, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}}})
@ ForwardDiff ~/.julia/packages/ForwardDiff/5gUap/src/apiutils.jl:44
[7] vector_mode_jacobian!(result::DiffResults.MutableDiffResult{1, Vector{Float64}, Tuple{Matrix{Float64}}}, f!::var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, y::Vector{Float64}, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}}})
@ ForwardDiff ~/.julia/packages/ForwardDiff/5gUap/src/jacobian.jl:172
[8] jacobian!(result::DiffResults.MutableDiffResult{1, Vector{Float64}, Tuple{Matrix{Float64}}}, f!::Function, y::Vector{Float64}, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}}}, ::Val{false})
@ ForwardDiff ~/.julia/packages/ForwardDiff/5gUap/src/jacobian.jl:78
[9] (::NLSolversBase.var"#fj_forwarddiff!#24"{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Vector{Float64}, ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#sys#7"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, Int64, var"#sys#6#8"}, Float64}, Float64, 2}}}}})(F::Vector{Float64}, J::Matrix{Float64}, x::Vector{Float64})
@ NLSolversBase ~/.julia/packages/NLSolversBase/GRQ1x/src/objective_types/oncedifferentiable.jl:160
[10] value_jacobian!!(obj::OnceDifferentiable{Vector{Float64}, Matrix{Float64}, Vector{Float64}}, F::Vector{Float64}, J::Matrix{Float64}, x::Vector{Float64})
@ NLSolversBase ~/.julia/packages/NLSolversBase/GRQ1x/src/interface.jl:124
[11] value_jacobian!!
@ ~/.julia/packages/NLSolversBase/GRQ1x/src/interface.jl:122 [inlined]
[12] trust_region_(df::OnceDifferentiable{Vector{Float64}, Matrix{Float64}, Vector{Float64}}, initial_x::Vector{Float64}, xtol::Float64, ftol::Float64, iterations::Int64, store_trace::Bool, show_trace::Bool, extended_trace::Bool, factor::Float64, autoscale::Bool, cache::NLsolve.NewtonTrustRegionCache{Vector{Float64}})
@ NLsolve ~/.julia/packages/NLsolve/gJL1I/src/solvers/trust_region.jl:119
[13] trust_region (repeats 2 times)
@ ~/.julia/packages/NLsolve/gJL1I/src/solvers/trust_region.jl:235 [inlined]
[14] nlsolve(df::OnceDifferentiable{Vector{Float64}, Matrix{Float64}, Vector{Float64}}, initial_x::Vector{Float64}; method::Symbol, xtol::Float64, ftol::Float64, iterations::Int64, store_trace::Bool, show_trace::Bool, extended_trace::Bool, linesearch::Static, linsolve::NLsolve.var"#29#31", factor::Float64, autoscale::Bool, m::Int64, beta::Int64, aa_start::Int64, droptol::Float64)
@ NLsolve ~/.julia/packages/NLsolve/gJL1I/src/nlsolve/nlsolve.jl:26
[15] nlsolve(f::Function, initial_x::Vector{Float64}; method::Symbol, autodiff::Symbol, inplace::Bool, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ NLsolve ~/.julia/packages/NLsolve/gJL1I/src/nlsolve/nlsolve.jl:52
[16] cd(; p::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}, i::Int64)
@ Main ./REPL[4]:12
[17] #9
@ ./REPL[5]:1 [inlined]
[18] vector_mode_dual_eval
@ ~/.julia/packages/ForwardDiff/5gUap/src/apiutils.jl:37 [inlined]
[19] vector_mode_jacobian(f::var"#9#10", x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}})
@ ForwardDiff ~/.julia/packages/ForwardDiff/5gUap/src/jacobian.jl:147
[20] jacobian(f::Function, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}}, ::Val{true})
@ ForwardDiff ~/.julia/packages/ForwardDiff/5gUap/src/jacobian.jl:21
[21] jacobian(f::Function, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#9#10", Float64}, Float64, 2}}}) (repeats 2 times)
@ ForwardDiff ~/.julia/packages/ForwardDiff/5gUap/src/jacobian.jl:19
[22] top-level scope
@ REPL[5]:1
```