Merge pull request #1256 from kapple19/#1085

Fix false positive result of passing a `Function` to `derivative`

Author: ChrisRackauckas

src/diff.jl

@@ -371,6 +371,9 @@ 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)
+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!"
     n = 1

test/diff.jl

@@ -378,4 +378,23 @@ let
     Dt = Differential(t)^0
     @test isequal(Dt, identity)
     test_equal(Dt(t + 2t^2), t + 2t^2)
-end
+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
+
+# 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