From 914c3152ae17abcbf28c99e9cbf842ffe4ea16d8 Mon Sep 17 00:00:00 2001
From: Aaron Kaw <aaronjkaw@gmail.com>
Date: Wed, 4 Sep 2024 08:41:50 +1000
Subject: [PATCH 1/4] Passing a Function to derivative now feeds the Num input
 to the function

---
 src/diff.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/diff.jl b/src/diff.jl
index d9d4c1bbf..a368e9c11 100644
--- a/src/diff.jl
+++ b/src/diff.jl
@@ -371,6 +371,8 @@ derivative(::typeof(+), args::NTuple{N,Any}, ::Val) where {N} = 1
 derivative(::typeof(*), args::NTuple{N,Any}, ::Val{i}) where {N,i} = *(deleteat!(collect(args), i)...)
 derivative(::typeof(one), args::Tuple{<:Any}, ::Val) = 0
 
+derivative(f::Function, x::Num) = derivative(f(x), x)
+
 function count_order(x)
     @assert !(x isa Symbol) "The variable $x must have an order of differentiation that is greater or equal to 1!"
     n = 1

From b7d75d0e988ca7163eab341c2c0f856266e1190e Mon Sep 17 00:00:00 2001
From: Aaron Kaw <aaronjkaw@gmail.com>
Date: Wed, 4 Sep 2024 08:50:34 +1000
Subject: [PATCH 2/4] Added tests to check if function inputs to derivative
 behave as expected

---
 test/diff.jl | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/test/diff.jl b/test/diff.jl
index 88956f138..23d9e837f 100644
--- a/test/diff.jl
+++ b/test/diff.jl
@@ -378,4 +378,15 @@ let
     Dt = Differential(t)^0
     @test isequal(Dt, identity)
     test_equal(Dt(t + 2t^2), t + 2t^2)
-end
\ No newline at end of file
+end
+
+# Check `Function` inputs for derivative (#1085)
+let
+    @variables x
+    @testset for f in [sqrt, sin, acos, exp, cis]
+        @test isequal(
+            Symbolics.derivative(f, x),
+            Symbolics.derivative(f(x), x)
+        )
+    end
+end

From 4d74c67546408fe93659faa9f9086be1447fa2c7 Mon Sep 17 00:00:00 2001
From: Aaron Kaw <aaronjkaw@gmail.com>
Date: Wed, 4 Sep 2024 09:10:15 +1000
Subject: [PATCH 3/4] derivative now throws for Function first input with
 non-Num second input

---
 src/diff.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/diff.jl b/src/diff.jl
index a368e9c11..891e2cde2 100644
--- a/src/diff.jl
+++ b/src/diff.jl
@@ -372,6 +372,7 @@ derivative(::typeof(*), args::NTuple{N,Any}, ::Val{i}) where {N,i} = *(deleteat!
 derivative(::typeof(one), args::Tuple{<:Any}, ::Val) = 0
 
 derivative(f::Function, x::Num) = derivative(f(x), x)
+derivative(::Function, x::Any) = TypeError(:derivative, "2nd argument", Num, typeof(x)) |> throw
 
 function count_order(x)
     @assert !(x isa Symbol) "The variable $x must have an order of differentiation that is greater or equal to 1!"

From 6fcede0ce0c012c9481f2a1c500c6fc69a6ba9e5 Mon Sep 17 00:00:00 2001
From: Aaron Kaw <aaronjkaw@gmail.com>
Date: Wed, 4 Sep 2024 09:23:11 +1000
Subject: [PATCH 4/4] Test derivative throws for Function then non-Num input

---
 test/diff.jl | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/test/diff.jl b/test/diff.jl
index 23d9e837f..eb500cb9d 100644
--- a/test/diff.jl
+++ b/test/diff.jl
@@ -390,3 +390,11 @@ let
         )
     end
 end
+
+# Check `Function` inputs throw for non-Num second input (#1085)
+let
+    @testset for f in [sqrt, sin, acos, exp, cis]
+        @test_throws TypeError Symbolics.derivative(f, rand())
+        @test_throws TypeError Symbolics.derivative(f, Val(rand(Int)))
+    end
+end