diff --git a/Project.toml b/Project.toml
index b6f204c..e6fa104 100644
--- a/Project.toml
+++ b/Project.toml
@@ -27,9 +27,11 @@ Unitful = "≥ 0.7.1"
 julia = "≥ 1.0.0"
 
 [extras]
+Calculus = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
 DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
 DiffEqDevTools = "f3b72e0c-5b89-59e1-b016-84e28bfd966d"
 DiffEqProblemLibrary = "a077e3f3-b75c-5d7f-a0c6-6bc4c8ec64a9"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
@@ -37,4 +39,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [targets]
-test = ["DiffEqCallbacks", "DiffEqDevTools", "DiffEqProblemLibrary", "Random", "RecursiveArrayTools", "SafeTestsets", "Test", "Unitful"]
+test = ["Calculus", "DiffEqCallbacks", "DiffEqDevTools", "DiffEqProblemLibrary", "LinearAlgebra", "Random", "RecursiveArrayTools", "SafeTestsets", "Test", "Unitful"]
diff --git a/test/differentiation.jl b/test/differentiation.jl
new file mode 100644
index 0000000..053dd60
--- /dev/null
+++ b/test/differentiation.jl
@@ -0,0 +1,56 @@
+using DelayDiffEq, Calculus, ForwardDiff
+using LinearAlgebra, Test
+
+# Hutchinson's equation
+function f(du, u, h, p, t)
+  du[1] = p[1] * u[1] * (1 - h(p, t - p[2])[1] / p[3])
+  nothing
+end
+
+h(p, t) = [p[4]]
+
+@testset "Gradient" begin
+  function test(p)
+    prob = DDEProblem(f, [p[5]], h, eltype(p).((0.0, 20.0)), copy(p);
+                      constant_lags = [p[2]])
+    sol = solve(prob, MethodOfSteps(Tsit5()); abstol = 1e-14, reltol = 1e-14)
+    diff = @. sol[1, :] - 10 * exp(-sol.t)
+    dot(diff, diff)
+  end
+
+  p = [1.0, 1.0, 1.0, 0.0, 1.0]
+  findiff = Calculus.finite_difference(test, p)
+  fordiff = @test_logs (:warn, r"^dt <= dtmin") ForwardDiff.gradient(test, p)
+
+  @test_broken findiff ≈ fordiff
+end
+
+@testset "Jacobian" begin
+  function test(p)
+    prob = DDEProblem(f, [p[5]], h, eltype(p).((0.0, 20.0)), copy(p);
+                      constant_lags = [p[2]])
+    solve(prob, MethodOfSteps(Tsit5()); abstol = 1e-14, reltol = 1e-14).u[end]
+  end
+
+  p = [1.0, 1.0, 1.0, 0.0, 1.0]
+  findiff = Calculus.finite_difference_jacobian(test, p)
+  fordiff = @test_logs (:warn, r"^dt <= dtmin") ForwardDiff.jacobian(test, p)
+
+  @test_broken findiff ≈ fordiff
+end
+
+@testset "Hessian" begin
+  function test(p)
+    prob = DDEProblem(f, [p[5]], h, eltype(p).((0.0, 20.0)), copy(p);
+                      constant_lags = [p[2]])
+    sol = solve(prob, MethodOfSteps(Tsit5()); abstol = 1e-14, reltol = 1e-14)
+    diff = @. sol[1, :] - 10 * exp(-sol.t)
+    dot(diff, diff)
+  end
+
+  p = [1.0, 1.0, 1.0, 0.0, 1.0]
+  findiff = Calculus.finite_difference_hessian(test, p)
+  fordiff = @test_logs (:warn, r"^dt <= dtmin") ForwardDiff.hessian(test, p)
+
+  @test_broken findiff ≈ fordiff
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index d8fb067..15f7b05 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -14,6 +14,7 @@ if GROUP == "All" || GROUP == "Interface"
   @time @safetestset "saveat Tests" begin include("saveat.jl") end
   @time @safetestset "save_idxs Tests" begin include("save_idxs.jl") end
   @time @safetestset "Event Tests" begin include("events.jl") end
+  @time @safetestset "Differentiation Tests" begin include("differentiation.jl") end
   @time @safetestset "Cache Tests" begin include("cache.jl") end
   @time @safetestset "Iterator Tests" begin include("iterator.jl") end
   @time @safetestset "Units Tests" begin include("units.jl") end