diff --git a/Project.toml b/Project.toml
index 64b7962a1..0c75bab01 100644
--- a/Project.toml
+++ b/Project.toml
@@ -22,7 +22,7 @@ ZygoteRules = "700de1a5-db45-46bc-99cf-38207098b444"
 
 [compat]
 AbstractFFTs = "0.5, 1.0"
-ChainRules = "0.7.45"
+ChainRules = "0.7.47"
 DiffRules = "1.0"
 FillArrays = "0.8, 0.9, 0.10, 0.11"
 ForwardDiff = "0.10"
diff --git a/src/lib/array.jl b/src/lib/array.jl
index 733026c84..102dc09c9 100644
--- a/src/lib/array.jl
+++ b/src/lib/array.jl
@@ -570,6 +570,14 @@ end
   return (Ā,)
 end
 
+# The adjoint for exp(::AbstractArray) intercepts ChainRules' rrule for exp(::Hermitian),
+# so we call it manually. This can be removed when the generic rule for exp is moved to
+# ChainRules
+@adjoint function exp(A::LinearAlgebra.RealHermSymComplexHerm)
+    Y, back = chain_rrule(exp, A)
+    return Y, Δ -> (back(Δ)[2],)
+end
+
 # Hermitian/Symmetric matrix functions that can be written as power series
 _realifydiag!(A::AbstractArray{<:Real}) = A
 function _realifydiag!(A)
@@ -581,10 +589,7 @@ function _realifydiag!(A)
 end
 @adjoint _realifydiag!(A) = _realifydiag!(A), Δ -> (_realifydiag!(Δ),)
 
-_hasrealdomain(f, x) = true
-_hasrealdomain(::Union{typeof.((acos,asin))...}, x) = all(x -> -1 ≤ x ≤ 1, x)
-_hasrealdomain(::typeof(acosh), x) = all(x -> x ≥ 1, x)
-_hasrealdomain(::Union{typeof.((log,sqrt,^))...}, x) = all(x -> x ≥ 0, x)
+_hasrealdomain(::typeof(^), x) = all(x -> x ≥ 0, x)
 
 _process_series_eigvals(f, λ) = _hasrealdomain(f, λ) ? λ : complex.(λ)
 
@@ -598,16 +603,6 @@ _process_series_matrix(::typeof(^), fA, ::Hermitian{<:Complex}, ::AbstractVector
 
 # Compute function on eigvals, thunks for conjugates of 1st and 2nd derivatives,
 # and function to pull back adjoints to args
-function _pullback_series_func_scalar(f, λ, args...)
-  compλ = _process_series_eigvals(f, λ)
-  fλ, fback = Zygote.pullback((x,args...) -> f.(x, args...), compλ, args...)
-  n = length(λ)
-  return (fλ,
-          ()->fback(ones(n))[1],
-          ()->nothing, # TODO: add 2nd deriv
-          isempty(args) ? _ -> () : f̄λ -> tail(fback(f̄λ)))
-end
-
 function _pullback_series_func_scalar(f::typeof(^), λ, p)
   compλ = _process_series_eigvals(f, λ)
   r, powλ = isinteger(p) ? (Integer(p), λ) : (p, compλ)
@@ -618,11 +613,6 @@ function _pullback_series_func_scalar(f::typeof(^), λ, p)
           f̄λ -> (dot(fλ .* log.(compλ), f̄λ),))
 end
 
-function _pullback_series_func_scalar(f::typeof(exp), λ)
-  expλ = exp.(λ)
-  return expλ, ()->expλ, ()->expλ, _ -> ()
-end
-
 _apply_series_func(f, A, args...) = f(A, args...)
 
 @adjoint function _apply_series_func(f, A, args...)
@@ -673,39 +663,6 @@ function _pullback(cx::AContext,
   return _pullback(cx, (A, p) -> _apply_series_func(f, A, p), A, p)
 end
 
-for func in (:exp, :log, :cos, :sin, :tan, :cosh, :sinh, :tanh, :acos, :asin, :atan, :acosh, :asinh, :atanh, :sqrt)
-  @eval begin
-    function _pullback(cx::AContext,
-                       f::typeof($func),
-                       A::LinearAlgebra.RealHermSymComplexHerm)
-      return _pullback(cx, A -> _apply_series_func(f, A), A)
-    end
-  end
-end
-
-@adjoint function sincos(A::LinearAlgebra.RealHermSymComplexHerm)
-  n = LinearAlgebra.checksquare(A)
-  λ, U = eigen(A)
-  sλ, cλ = Buffer(λ), Buffer(λ)
-  for i in Base.OneTo(n)
-    @inbounds sλ[i], cλ[i] = sincos(λ[i])
-  end
-  sinλ, cosλ = copy(sλ), copy(cλ)
-  sinA, cosA = U * Diagonal(sinλ) * U', U * Diagonal(cosλ) * U'
-  Ω, processback = Zygote.pullback(sinA, cosA) do s,c
-    return (_process_series_matrix(sin, s, A, λ),
-            _process_series_matrix(cos, c, A, λ))
-  end
-  return Ω, function (Ω̄)
-    s̄inA, c̄osA = processback(Ω̄)
-    s̄inΛ, c̄osΛ = U' * s̄inA * U, U' * c̄osA * U
-    PS = _pairdiffquotmat(sin, n, λ, sinλ, cosλ, -sinλ)
-    PC = _pairdiffquotmat(cos, n, λ, cosλ, -sinλ, -cosλ)
-    Ā = U * (PS .* s̄inΛ .+ PC .* c̄osΛ) * U'
-    return (Ā,)
-  end
-end
-
 # ChainRules has this also but does not use FillArrays, so we have our own definition
 # for improved performance. See https://github.com/JuliaDiff/ChainRules.jl/issues/46
 Zygote.@adjoint function LinearAlgebra.tr(x::AbstractMatrix)
diff --git a/test/gradcheck.jl b/test/gradcheck.jl
index d36ea68fc..a23a52aeb 100644
--- a/test/gradcheck.jl
+++ b/test/gradcheck.jl
@@ -865,10 +865,17 @@ _randmatseries(rng, ::typeof(atanh), T, n, domain::Type{Complex}) = nothing
 
         @test _gradtest_hermsym(f, ST, A)
 
-        y = Zygote.pullback(f, A)[1]
+        y, back = Zygote.pullback(f, A)
         y2 = f(A)
         @test y ≈ y2
         @test typeof(y) == typeof(y2)
+        ȳ = randn(eltype(y), size(y))
+        if y isa Union{Symmetric,Hermitian}
+            ȳ = typeof(y)(ȳ, y.uplo)
+        end
+        Ā = back(ȳ)[1]
+        @test typeof(Ā) == typeof(A)
+        @test Ā.uplo == A.uplo
 
         @testset "similar eigenvalues" begin
           λ[1] = λ[3] + sqrt(eps(eltype(λ))) / 10