Differentiation of eigen(::Symmetric)

[KnutAM]

This seemed nicely solved by @dlfivefifty in #513 (Discussed in #111 ), but I got an error when applying to the eigen function and not the eigvals functions that was tested.

f(x) = eigen(Symmetric(x*x')).vectors[:,1];
x0 = [1.,2.];
ForwardDiff.jacobian(f, x0)
ERROR: type Array has no field dv
Stacktrace:
 [1] getproperty
   @ .\Base.jl:42 [inlined]
 [2] eigen(A::Symmetric{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}, Matrix{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}}})
   @ ForwardDiff C:\Users\meyer\.julia\packages\ForwardDiff\PBzup\src\dual.jl:685
 [3] f(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}})
   @ Main .\REPL[37]:1
 [4] vector_mode_dual_eval!(f::typeof(f), cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}}}, x::Vector{Float64})
   @ ForwardDiff C:\Users\meyer\.julia\packages\ForwardDiff\PBzup\src\apiutils.jl:37
 [5] vector_mode_jacobian(f::typeof(f), x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}}})   @ ForwardDiff C:\Users\meyer\.julia\packages\ForwardDiff\PBzup\src\jacobian.jl:148
 [6] jacobian(f::Function, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}}}, ::Val{true})   @ ForwardDiff C:\Users\meyer\.julia\packages\ForwardDiff\PBzup\src\jacobian.jl:21
 [7] jacobian(f::Function, x::Vector{Float64}, cfg::ForwardDiff.JacobianConfig{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 2}}}) (repeats 2 times)
   @ ForwardDiff C:\Users\meyer\.julia\packages\ForwardDiff\PBzup\src\jacobian.jl:19
 [8] top-level scope
   @ REPL[39]:1

This PR takes the original code suggested in #111, as I think there is a mixup between SymTridiagonal and Symmetric in the current implementation in master.
Edit: It also enables the differentiation of a Symmetric StaticMatrix.

[codecov-commenter]

Codecov Report

Merging #575 (85c79a0) into master (29332b1) will increase coverage by 1.17%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #575      +/-   ##
==========================================
+ Coverage   85.39%   86.57%   +1.17%     
==========================================
  Files           9        9              
  Lines         856      894      +38     
==========================================
+ Hits          731      774      +43     
+ Misses        125      120       -5     

Impacted Files	Coverage Δ
src/dual.jl	79.21% <100.00%> (+4.72%)	⬆️
src/derivative.jl	94.44% <0.00%> (-5.56%)	⬇️

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[KnutAM]

@andreasnoack, since you reviewed #513, may I ask for your opinion on this one?