diff --git a/src/derivatives.jl b/src/derivatives.jl
index 2ec303df..2cc5d33e 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -20,20 +20,28 @@ function _extrapolate_derivative_left(A, t, order)
     elseif extrapolation_left == ExtrapolationType.Constant
         zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_left == ExtrapolationType.Linear
-        (order == 1) ? derivative(A, first(A.t)) : zero(first(A.u) / one(A.t[1]))
+        _derivative(A, first(A.t), 1)
+        zero(first(A.u) / one(A.t[1]))
+        (order == 1) ? _derivative(A, first(A.t), 1) : zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_left == ExtrapolationType.Extension
-        iguess = A.iguesser
-        (order == 1) ? _derivative(A, t, iguess) :
+        (order == 1) ? _derivative(A, t, length(A.t)) :
         ForwardDiff.derivative(t -> begin
-                _derivative(A, t, iguess)
+                _derivative(A, t, length(A.t))
             end, t)
     elseif extrapolation_left == ExtrapolationType.Periodic
         t_, _ = transformation_periodic(A, t)
-        derivative(A, t_, order)
+        (order == 1) ? _derivative(A, t_, A.iguesser) :
+        ForwardDiff.derivative(t -> begin
+                _derivative(A, t, A.iguesser)
+            end, t_)
     else
         # extrapolation_left == ExtrapolationType.Reflective
         t_, n = transformation_reflective(A, t)
-        isodd(n) ? -derivative(A, t_, order) : derivative(A, t_, order)
+        sign = isodd(n) ? -1 : 1
+        (order == 1) ? sign * _derivative(A, t_, A.iguesser) :
+        ForwardDiff.derivative(t -> begin
+                sign * _derivative(A, t, A.iguesser)
+            end, t_)
     end
 end
 
@@ -44,20 +52,27 @@ function _extrapolate_derivative_right(A, t, order)
     elseif extrapolation_right == ExtrapolationType.Constant
         zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_right == ExtrapolationType.Linear
-        (order == 1) ? derivative(A, last(A.t)) : zero(first(A.u) / one(A.t[1]))
+        (order == 1) ? _derivative(A, last(A.t), length(A.t)) :
+        zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_right == ExtrapolationType.Extension
-        iguess = A.iguesser
-        (order == 1) ? _derivative(A, t, iguess) :
+        (order == 1) ? _derivative(A, t, length(A.t)) :
         ForwardDiff.derivative(t -> begin
-                _derivative(A, t, iguess)
+                _derivative(A, t, length(A.t))
             end, t)
     elseif extrapolation_right == ExtrapolationType.Periodic
         t_, _ = transformation_periodic(A, t)
-        derivative(A, t_, order)
+        (order == 1) ? _derivative(A, t_, A.iguesser) :
+        ForwardDiff.derivative(t -> begin
+                _derivative(A, t, A.iguesser)
+            end, t_)
     else
-        # extrapolation_right == ExtrapolationType.Reflective
+        # extrapolation_left == ExtrapolationType.Reflective
         t_, n = transformation_reflective(A, t)
-        iseven(n) ? -derivative(A, t_, order) : derivative(A, t_, order)
+        sign = iseven(n) ? -1 : 1
+        (order == 1) ? sign * _derivative(A, t_, A.iguesser) :
+        ForwardDiff.derivative(t -> begin
+                sign * _derivative(A, t, A.iguesser)
+            end, t_)
     end
 end
 
@@ -299,4 +314,4 @@ function _derivative(
     out += Δt₀^2 *
            (3c₁ + (3Δt₁ + Δt₀) * c₂ + (3Δt₁^2 + Δt₀ * 2Δt₁) * c₃)
     out
-end
+end
\ No newline at end of file
diff --git a/src/integral_inverses.jl b/src/integral_inverses.jl
index a11d278d..22fde725 100644
--- a/src/integral_inverses.jl
+++ b/src/integral_inverses.jl
@@ -13,12 +13,12 @@ Creates the inverted integral interpolation object from the given interpolation.
 
   - `A`: interpolation object satisfying the above requirements
 """
-invert_integral(A::AbstractInterpolation) = throw(IntegralInverseNotFoundError())
+invert_integral(::AbstractInterpolation) = throw(IntegralInverseNotFoundError())
 
-_integral(A::AbstractIntegralInverseInterpolation, idx, t) = throw(IntegralNotFoundError())
+_integral(::AbstractIntegralInverseInterpolation, idx, t) = throw(IntegralNotFoundError())
 
 function _derivative(A::AbstractIntegralInverseInterpolation, t::Number, iguess)
-    inv(A.itp(A(t)))
+    inv(A.itp(_interpolate(A, t, iguess)))
 end
 
 """
@@ -119,4 +119,4 @@ function _interpolate(
         idx_ = get_idx(A, t, idx; side = :first, lb = 1, ub_shift = 0)
     end
     A.u[idx] + (t - A.t[idx]) / A.itp.u[idx_]
-end
+end
\ No newline at end of file
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index f2dd80ad..f8cdce89 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -13,10 +13,10 @@ function _extrapolate_left(A, t)
     if extrapolation_left == ExtrapolationType.None
         throw(LeftExtrapolationError())
     elseif extrapolation_left == ExtrapolationType.Constant
-        slope = derivative(A, first(A.t))
+        slope = _derivative(A, first(A.t), 1)
         first(A.u) + zero(slope * t)
     elseif extrapolation_left == ExtrapolationType.Linear
-        slope = derivative(A, first(A.t))
+        slope = _derivative(A, first(A.t), 1)
         first(A.u) + slope * (t - first(A.t))
     else
         _extrapolate_other(A, t, extrapolation_left)
@@ -28,10 +28,10 @@ function _extrapolate_right(A, t)
     if extrapolation_right == ExtrapolationType.None
         throw(RightExtrapolationError())
     elseif extrapolation_right == ExtrapolationType.Constant
-        slope = derivative(A, last(A.t))
+        slope = _derivative(A, last(A.t), length(A.t))
         last(A.u) + zero(slope * t)
     elseif extrapolation_right == ExtrapolationType.Linear
-        slope = derivative(A, last(A.t))
+        slope = _derivative(A, last(A.t), length(A.t))
         last(A.u) + slope * (t - last(A.t))
     else
         _extrapolate_other(A, t, extrapolation_right)
@@ -335,4 +335,4 @@ function _interpolate(
     c₁, c₂, c₃ = get_parameters(A, idx)
     out += Δt₀^3 * (c₁ + Δt₁ * (c₂ + c₃ * Δt₁))
     out
-end
+end
\ No newline at end of file
diff --git a/test/integral_inverse_tests.jl b/test/integral_inverse_tests.jl
index 494e4943..6b09f9cd 100644
--- a/test/integral_inverse_tests.jl
+++ b/test/integral_inverse_tests.jl
@@ -17,6 +17,8 @@ function test_integral_inverses(method; args = [], kwargs = [])
         adiff = derivative(A_intinv, I)
         @test cdiff ≈ adiff
     end
+
+    @test @inferred(A(ts[37])) == A(ts[37])
 end
 
 @testset "Linear Interpolation" begin