analysis.special_functions.exp_deriv ⟷ Mathlib.Analysis.SpecialFunctions.ExpDeriv

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -37,7 +37,7 @@ theorem hasDerivAt_exp (x : ℂ) : HasDerivAt exp (exp x) x :=
   by
   rw [hasDerivAt_iff_isLittleO_nhds_zero]
   have : (1 : ℕ) < 2 := by norm_num
-  refine' (is_O.of_bound ‖exp x‖ _).trans_isLittleO (is_o_pow_id this)
+  refine' (is_O.of_bound ‖NormedSpace.exp x‖ _).trans_isLittleO (is_o_pow_id this)
   filter_upwards [Metric.ball_mem_nhds (0 : ℂ) zero_lt_one]
   simp only [Metric.mem_ball, dist_zero_right, norm_pow]
   exact fun z hz => exp_bound_sq x z hz.le
@@ -75,7 +75,8 @@ theorem iter_deriv_exp : ∀ n : ℕ, (deriv^[n]) exp = exp
 theorem contDiff_exp : ∀ {n}, ContDiff 𝕜 n exp :=
   by
   refine' contDiff_all_iff_nat.2 fun n => _
-  have : ContDiff ℂ (↑n) exp := by
+  have : ContDiff ℂ (↑n) NormedSpace.exp :=
+    by
     induction' n with n ihn
     · exact contDiff_zero.2 continuous_exp
     · rw [contDiff_succ_iff_deriv]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,7 +3,7 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
 -/
-import Mathbin.Analysis.Complex.RealDeriv
+import Analysis.Complex.RealDeriv
 
 #align_import analysis.special_functions.exp_deriv from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-
-! This file was ported from Lean 3 source module analysis.special_functions.exp_deriv
-! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Complex.RealDeriv
 
+#align_import analysis.special_functions.exp_deriv from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
+
 /-!
 # Complex and real exponential
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -34,6 +34,7 @@ namespace Complex
 
 variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ]
 
+#print Complex.hasDerivAt_exp /-
 /-- The complex exponential is everywhere differentiable, with the derivative `exp x`. -/
 theorem hasDerivAt_exp (x : ℂ) : HasDerivAt exp (exp x) x :=
   by
@@ -44,26 +45,36 @@ theorem hasDerivAt_exp (x : ℂ) : HasDerivAt exp (exp x) x :=
   simp only [Metric.mem_ball, dist_zero_right, norm_pow]
   exact fun z hz => exp_bound_sq x z hz.le
 #align complex.has_deriv_at_exp Complex.hasDerivAt_exp
+-/
 
+#print Complex.differentiable_exp /-
 theorem differentiable_exp : Differentiable 𝕜 exp := fun x =>
   (hasDerivAt_exp x).DifferentiableAt.restrictScalars 𝕜
 #align complex.differentiable_exp Complex.differentiable_exp
+-/
 
+#print Complex.differentiableAt_exp /-
 theorem differentiableAt_exp {x : ℂ} : DifferentiableAt 𝕜 exp x :=
   differentiable_exp x
 #align complex.differentiable_at_exp Complex.differentiableAt_exp
+-/
 
+#print Complex.deriv_exp /-
 @[simp]
 theorem deriv_exp : deriv exp = exp :=
   funext fun x => (hasDerivAt_exp x).deriv
 #align complex.deriv_exp Complex.deriv_exp
+-/
 
+#print Complex.iter_deriv_exp /-
 @[simp]
 theorem iter_deriv_exp : ∀ n : ℕ, (deriv^[n]) exp = exp
   | 0 => rfl
   | n + 1 => by rw [iterate_succ_apply, deriv_exp, iter_deriv_exp n]
 #align complex.iter_deriv_exp Complex.iter_deriv_exp
+-/
 
+#print Complex.contDiff_exp /-
 theorem contDiff_exp : ∀ {n}, ContDiff 𝕜 n exp :=
   by
   refine' contDiff_all_iff_nat.2 fun n => _
@@ -75,14 +86,19 @@ theorem contDiff_exp : ∀ {n}, ContDiff 𝕜 n exp :=
       rwa [deriv_exp]
   exact this.restrict_scalars 𝕜
 #align complex.cont_diff_exp Complex.contDiff_exp
+-/
 
+#print Complex.hasStrictDerivAt_exp /-
 theorem hasStrictDerivAt_exp (x : ℂ) : HasStrictDerivAt exp (exp x) x :=
   contDiff_exp.ContDiffAt.hasStrictDerivAt' (hasDerivAt_exp x) le_rfl
 #align complex.has_strict_deriv_at_exp Complex.hasStrictDerivAt_exp
+-/
 
+#print Complex.hasStrictFDerivAt_exp_real /-
 theorem hasStrictFDerivAt_exp_real (x : ℂ) : HasStrictFDerivAt exp (exp x • (1 : ℂ →L[ℝ] ℂ)) x :=
   (hasStrictDerivAt_exp x).complexToReal_fderiv
 #align complex.has_strict_fderiv_at_exp_real Complex.hasStrictFDerivAt_exp_real
+-/
 
 end Complex
 
@@ -91,31 +107,41 @@ section
 variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ] {f : 𝕜 → ℂ} {f' : ℂ} {x : 𝕜}
   {s : Set 𝕜}
 
+#print HasStrictDerivAt.cexp /-
 theorem HasStrictDerivAt.cexp (hf : HasStrictDerivAt f f' x) :
     HasStrictDerivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) * f') x :=
   (Complex.hasStrictDerivAt_exp (f x)).comp x hf
 #align has_strict_deriv_at.cexp HasStrictDerivAt.cexp
+-/
 
+#print HasDerivAt.cexp /-
 theorem HasDerivAt.cexp (hf : HasDerivAt f f' x) :
     HasDerivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) * f') x :=
   (Complex.hasDerivAt_exp (f x)).comp x hf
 #align has_deriv_at.cexp HasDerivAt.cexp
+-/
 
+#print HasDerivWithinAt.cexp /-
 theorem HasDerivWithinAt.cexp (hf : HasDerivWithinAt f f' s x) :
     HasDerivWithinAt (fun x => Complex.exp (f x)) (Complex.exp (f x) * f') s x :=
   (Complex.hasDerivAt_exp (f x)).comp_hasDerivWithinAt x hf
 #align has_deriv_within_at.cexp HasDerivWithinAt.cexp
+-/
 
+#print derivWithin_cexp /-
 theorem derivWithin_cexp (hf : DifferentiableWithinAt 𝕜 f s x) (hxs : UniqueDiffWithinAt 𝕜 s x) :
     derivWithin (fun x => Complex.exp (f x)) s x = Complex.exp (f x) * derivWithin f s x :=
   hf.HasDerivWithinAt.cexp.derivWithin hxs
 #align deriv_within_cexp derivWithin_cexp
+-/
 
+#print deriv_cexp /-
 @[simp]
 theorem deriv_cexp (hc : DifferentiableAt 𝕜 f x) :
     deriv (fun x => Complex.exp (f x)) x = Complex.exp (f x) * deriv f x :=
   hc.HasDerivAt.cexp.deriv
 #align deriv_cexp deriv_cexp
+-/
 
 end
 
@@ -124,59 +150,81 @@ section
 variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ] {E : Type _}
   [NormedAddCommGroup E] [NormedSpace 𝕜 E] {f : E → ℂ} {f' : E →L[𝕜] ℂ} {x : E} {s : Set E}
 
+#print HasStrictFDerivAt.cexp /-
 theorem HasStrictFDerivAt.cexp (hf : HasStrictFDerivAt f f' x) :
     HasStrictFDerivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') x :=
   (Complex.hasStrictDerivAt_exp (f x)).comp_hasStrictFDerivAt x hf
 #align has_strict_fderiv_at.cexp HasStrictFDerivAt.cexp
+-/
 
+#print HasFDerivWithinAt.cexp /-
 theorem HasFDerivWithinAt.cexp (hf : HasFDerivWithinAt f f' s x) :
     HasFDerivWithinAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') s x :=
   (Complex.hasDerivAt_exp (f x)).comp_hasFDerivWithinAt x hf
 #align has_fderiv_within_at.cexp HasFDerivWithinAt.cexp
+-/
 
+#print HasFDerivAt.cexp /-
 theorem HasFDerivAt.cexp (hf : HasFDerivAt f f' x) :
     HasFDerivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') x :=
   hasFDerivWithinAt_univ.1 <| hf.HasFDerivWithinAt.cexp
 #align has_fderiv_at.cexp HasFDerivAt.cexp
+-/
 
+#print DifferentiableWithinAt.cexp /-
 theorem DifferentiableWithinAt.cexp (hf : DifferentiableWithinAt 𝕜 f s x) :
     DifferentiableWithinAt 𝕜 (fun x => Complex.exp (f x)) s x :=
   hf.HasFDerivWithinAt.cexp.DifferentiableWithinAt
 #align differentiable_within_at.cexp DifferentiableWithinAt.cexp
+-/
 
+#print DifferentiableAt.cexp /-
 @[simp]
 theorem DifferentiableAt.cexp (hc : DifferentiableAt 𝕜 f x) :
     DifferentiableAt 𝕜 (fun x => Complex.exp (f x)) x :=
   hc.HasFDerivAt.cexp.DifferentiableAt
 #align differentiable_at.cexp DifferentiableAt.cexp
+-/
 
+#print DifferentiableOn.cexp /-
 theorem DifferentiableOn.cexp (hc : DifferentiableOn 𝕜 f s) :
     DifferentiableOn 𝕜 (fun x => Complex.exp (f x)) s := fun x h => (hc x h).cexp
 #align differentiable_on.cexp DifferentiableOn.cexp
+-/
 
+#print Differentiable.cexp /-
 @[simp]
 theorem Differentiable.cexp (hc : Differentiable 𝕜 f) :
     Differentiable 𝕜 fun x => Complex.exp (f x) := fun x => (hc x).cexp
 #align differentiable.cexp Differentiable.cexp
+-/
 
+#print ContDiff.cexp /-
 theorem ContDiff.cexp {n} (h : ContDiff 𝕜 n f) : ContDiff 𝕜 n fun x => Complex.exp (f x) :=
   Complex.contDiff_exp.comp h
 #align cont_diff.cexp ContDiff.cexp
+-/
 
+#print ContDiffAt.cexp /-
 theorem ContDiffAt.cexp {n} (hf : ContDiffAt 𝕜 n f x) :
     ContDiffAt 𝕜 n (fun x => Complex.exp (f x)) x :=
   Complex.contDiff_exp.ContDiffAt.comp x hf
 #align cont_diff_at.cexp ContDiffAt.cexp
+-/
 
+#print ContDiffOn.cexp /-
 theorem ContDiffOn.cexp {n} (hf : ContDiffOn 𝕜 n f s) :
     ContDiffOn 𝕜 n (fun x => Complex.exp (f x)) s :=
   Complex.contDiff_exp.comp_contDiffOn hf
 #align cont_diff_on.cexp ContDiffOn.cexp
+-/
 
+#print ContDiffWithinAt.cexp /-
 theorem ContDiffWithinAt.cexp {n} (hf : ContDiffWithinAt 𝕜 n f s x) :
     ContDiffWithinAt 𝕜 n (fun x => Complex.exp (f x)) s x :=
   Complex.contDiff_exp.ContDiffAt.comp_contDiffWithinAt x hf
 #align cont_diff_within_at.cexp ContDiffWithinAt.cexp
+-/
 
 end
 
@@ -238,31 +286,41 @@ function, for standalone use and use with `simp`. -/
 
 variable {f : ℝ → ℝ} {f' x : ℝ} {s : Set ℝ}
 
+#print HasStrictDerivAt.exp /-
 theorem HasStrictDerivAt.exp (hf : HasStrictDerivAt f f' x) :
     HasStrictDerivAt (fun x => Real.exp (f x)) (Real.exp (f x) * f') x :=
   (Real.hasStrictDerivAt_exp (f x)).comp x hf
 #align has_strict_deriv_at.exp HasStrictDerivAt.exp
+-/
 
+#print HasDerivAt.exp /-
 theorem HasDerivAt.exp (hf : HasDerivAt f f' x) :
     HasDerivAt (fun x => Real.exp (f x)) (Real.exp (f x) * f') x :=
   (Real.hasDerivAt_exp (f x)).comp x hf
 #align has_deriv_at.exp HasDerivAt.exp
+-/
 
+#print HasDerivWithinAt.exp /-
 theorem HasDerivWithinAt.exp (hf : HasDerivWithinAt f f' s x) :
     HasDerivWithinAt (fun x => Real.exp (f x)) (Real.exp (f x) * f') s x :=
   (Real.hasDerivAt_exp (f x)).comp_hasDerivWithinAt x hf
 #align has_deriv_within_at.exp HasDerivWithinAt.exp
+-/
 
+#print derivWithin_exp /-
 theorem derivWithin_exp (hf : DifferentiableWithinAt ℝ f s x) (hxs : UniqueDiffWithinAt ℝ s x) :
     derivWithin (fun x => Real.exp (f x)) s x = Real.exp (f x) * derivWithin f s x :=
   hf.HasDerivWithinAt.exp.derivWithin hxs
 #align deriv_within_exp derivWithin_exp
+-/
 
+#print deriv_exp /-
 @[simp]
 theorem deriv_exp (hc : DifferentiableAt ℝ f x) :
     deriv (fun x => Real.exp (f x)) x = Real.exp (f x) * deriv f x :=
   hc.HasDerivAt.exp.deriv
 #align deriv_exp deriv_exp
+-/
 
 end
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
 
 ! This file was ported from Lean 3 source module analysis.special_functions.exp_deriv
-! leanprover-community/mathlib commit 6a5c85000ab93fe5dcfdf620676f614ba8e18c26
+! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Complex.RealDeriv
 /-!
 # Complex and real exponential
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that `complex.exp` and `real.exp` are infinitely smooth functions.
 
 ## Tags

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -181,35 +181,49 @@ namespace Real
 
 variable {x y z : ℝ}
 
+#print Real.hasStrictDerivAt_exp /-
 theorem hasStrictDerivAt_exp (x : ℝ) : HasStrictDerivAt exp (exp x) x :=
   (Complex.hasStrictDerivAt_exp x).real_of_complex
 #align real.has_strict_deriv_at_exp Real.hasStrictDerivAt_exp
+-/
 
+#print Real.hasDerivAt_exp /-
 theorem hasDerivAt_exp (x : ℝ) : HasDerivAt exp (exp x) x :=
   (Complex.hasDerivAt_exp x).real_of_complex
 #align real.has_deriv_at_exp Real.hasDerivAt_exp
+-/
 
+#print Real.contDiff_exp /-
 theorem contDiff_exp {n} : ContDiff ℝ n exp :=
   Complex.contDiff_exp.real_of_complex
 #align real.cont_diff_exp Real.contDiff_exp
+-/
 
+#print Real.differentiable_exp /-
 theorem differentiable_exp : Differentiable ℝ exp := fun x => (hasDerivAt_exp x).DifferentiableAt
 #align real.differentiable_exp Real.differentiable_exp
+-/
 
+#print Real.differentiableAt_exp /-
 theorem differentiableAt_exp : DifferentiableAt ℝ exp x :=
   differentiable_exp x
 #align real.differentiable_at_exp Real.differentiableAt_exp
+-/
 
+#print Real.deriv_exp /-
 @[simp]
 theorem deriv_exp : deriv exp = exp :=
   funext fun x => (hasDerivAt_exp x).deriv
 #align real.deriv_exp Real.deriv_exp
+-/
 
+#print Real.iter_deriv_exp /-
 @[simp]
 theorem iter_deriv_exp : ∀ n : ℕ, (deriv^[n]) exp = exp
   | 0 => rfl
   | n + 1 => by rw [iterate_succ_apply, deriv_exp, iter_deriv_exp n]
 #align real.iter_deriv_exp Real.iter_deriv_exp
+-/
 
 end Real
 
@@ -258,68 +272,94 @@ function, for standalone use and use with `simp`. -/
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {f' : E →L[ℝ] ℝ} {x : E}
   {s : Set E}
 
+#print ContDiff.exp /-
 theorem ContDiff.exp {n} (hf : ContDiff ℝ n f) : ContDiff ℝ n fun x => Real.exp (f x) :=
   Real.contDiff_exp.comp hf
 #align cont_diff.exp ContDiff.exp
+-/
 
+#print ContDiffAt.exp /-
 theorem ContDiffAt.exp {n} (hf : ContDiffAt ℝ n f x) : ContDiffAt ℝ n (fun x => Real.exp (f x)) x :=
   Real.contDiff_exp.ContDiffAt.comp x hf
 #align cont_diff_at.exp ContDiffAt.exp
+-/
 
+#print ContDiffOn.exp /-
 theorem ContDiffOn.exp {n} (hf : ContDiffOn ℝ n f s) : ContDiffOn ℝ n (fun x => Real.exp (f x)) s :=
   Real.contDiff_exp.comp_contDiffOn hf
 #align cont_diff_on.exp ContDiffOn.exp
+-/
 
+#print ContDiffWithinAt.exp /-
 theorem ContDiffWithinAt.exp {n} (hf : ContDiffWithinAt ℝ n f s x) :
     ContDiffWithinAt ℝ n (fun x => Real.exp (f x)) s x :=
   Real.contDiff_exp.ContDiffAt.comp_contDiffWithinAt x hf
 #align cont_diff_within_at.exp ContDiffWithinAt.exp
+-/
 
+#print HasFDerivWithinAt.exp /-
 theorem HasFDerivWithinAt.exp (hf : HasFDerivWithinAt f f' s x) :
     HasFDerivWithinAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') s x :=
   (Real.hasDerivAt_exp (f x)).comp_hasFDerivWithinAt x hf
 #align has_fderiv_within_at.exp HasFDerivWithinAt.exp
+-/
 
+#print HasFDerivAt.exp /-
 theorem HasFDerivAt.exp (hf : HasFDerivAt f f' x) :
     HasFDerivAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') x :=
   (Real.hasDerivAt_exp (f x)).comp_hasFDerivAt x hf
 #align has_fderiv_at.exp HasFDerivAt.exp
+-/
 
+#print HasStrictFDerivAt.exp /-
 theorem HasStrictFDerivAt.exp (hf : HasStrictFDerivAt f f' x) :
     HasStrictFDerivAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') x :=
   (Real.hasStrictDerivAt_exp (f x)).comp_hasStrictFDerivAt x hf
 #align has_strict_fderiv_at.exp HasStrictFDerivAt.exp
+-/
 
+#print DifferentiableWithinAt.exp /-
 theorem DifferentiableWithinAt.exp (hf : DifferentiableWithinAt ℝ f s x) :
     DifferentiableWithinAt ℝ (fun x => Real.exp (f x)) s x :=
   hf.HasFDerivWithinAt.exp.DifferentiableWithinAt
 #align differentiable_within_at.exp DifferentiableWithinAt.exp
+-/
 
+#print DifferentiableAt.exp /-
 @[simp]
 theorem DifferentiableAt.exp (hc : DifferentiableAt ℝ f x) :
     DifferentiableAt ℝ (fun x => Real.exp (f x)) x :=
   hc.HasFDerivAt.exp.DifferentiableAt
 #align differentiable_at.exp DifferentiableAt.exp
+-/
 
+#print DifferentiableOn.exp /-
 theorem DifferentiableOn.exp (hc : DifferentiableOn ℝ f s) :
     DifferentiableOn ℝ (fun x => Real.exp (f x)) s := fun x h => (hc x h).exp
 #align differentiable_on.exp DifferentiableOn.exp
+-/
 
+#print Differentiable.exp /-
 @[simp]
 theorem Differentiable.exp (hc : Differentiable ℝ f) : Differentiable ℝ fun x => Real.exp (f x) :=
   fun x => (hc x).exp
 #align differentiable.exp Differentiable.exp
+-/
 
+#print fderivWithin_exp /-
 theorem fderivWithin_exp (hf : DifferentiableWithinAt ℝ f s x) (hxs : UniqueDiffWithinAt ℝ s x) :
     fderivWithin ℝ (fun x => Real.exp (f x)) s x = Real.exp (f x) • fderivWithin ℝ f s x :=
   hf.HasFDerivWithinAt.exp.fderivWithin hxs
 #align fderiv_within_exp fderivWithin_exp
+-/
 
+#print fderiv_exp /-
 @[simp]
 theorem fderiv_exp (hc : DifferentiableAt ℝ f x) :
     fderiv ℝ (fun x => Real.exp (f x)) x = Real.exp (f x) • fderiv ℝ f x :=
   hc.HasFDerivAt.exp.fderiv
 #align fderiv_exp fderiv_exp
+-/
 
 end
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -4,11 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
 
 ! This file was ported from Lean 3 source module analysis.special_functions.exp_deriv
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit 6a5c85000ab93fe5dcfdf620676f614ba8e18c26
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.Calculus.Inverse
 import Mathbin.Analysis.Complex.RealDeriv
 
 /-!
@@ -75,17 +74,13 @@ theorem contDiff_exp : ∀ {n}, ContDiff 𝕜 n exp :=
 #align complex.cont_diff_exp Complex.contDiff_exp
 
 theorem hasStrictDerivAt_exp (x : ℂ) : HasStrictDerivAt exp (exp x) x :=
-  contDiff_exp.ContDiffAt.has_strict_deriv_at' (hasDerivAt_exp x) le_rfl
+  contDiff_exp.ContDiffAt.hasStrictDerivAt' (hasDerivAt_exp x) le_rfl
 #align complex.has_strict_deriv_at_exp Complex.hasStrictDerivAt_exp
 
 theorem hasStrictFDerivAt_exp_real (x : ℂ) : HasStrictFDerivAt exp (exp x • (1 : ℂ →L[ℝ] ℂ)) x :=
   (hasStrictDerivAt_exp x).complexToReal_fderiv
 #align complex.has_strict_fderiv_at_exp_real Complex.hasStrictFDerivAt_exp_real
 
-theorem isOpenMap_exp : IsOpenMap exp :=
-  open_map_of_strict_deriv hasStrictDerivAt_exp exp_ne_zero
-#align complex.is_open_map_exp Complex.isOpenMap_exp
-
 end Complex
 
 section

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -26,7 +26,7 @@ noncomputable section
 
 open Filter Asymptotics Set Function
 
-open Classical Topology
+open scoped Classical Topology
 
 namespace Complex
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -78,9 +78,9 @@ theorem hasStrictDerivAt_exp (x : ℂ) : HasStrictDerivAt exp (exp x) x :=
   contDiff_exp.ContDiffAt.has_strict_deriv_at' (hasDerivAt_exp x) le_rfl
 #align complex.has_strict_deriv_at_exp Complex.hasStrictDerivAt_exp
 
-theorem hasStrictFderivAt_exp_real (x : ℂ) : HasStrictFderivAt exp (exp x • (1 : ℂ →L[ℝ] ℂ)) x :=
+theorem hasStrictFDerivAt_exp_real (x : ℂ) : HasStrictFDerivAt exp (exp x • (1 : ℂ →L[ℝ] ℂ)) x :=
   (hasStrictDerivAt_exp x).complexToReal_fderiv
-#align complex.has_strict_fderiv_at_exp_real Complex.hasStrictFderivAt_exp_real
+#align complex.has_strict_fderiv_at_exp_real Complex.hasStrictFDerivAt_exp_real
 
 theorem isOpenMap_exp : IsOpenMap exp :=
   open_map_of_strict_deriv hasStrictDerivAt_exp exp_ne_zero
@@ -126,30 +126,30 @@ section
 variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ] {E : Type _}
   [NormedAddCommGroup E] [NormedSpace 𝕜 E] {f : E → ℂ} {f' : E →L[𝕜] ℂ} {x : E} {s : Set E}
 
-theorem HasStrictFderivAt.cexp (hf : HasStrictFderivAt f f' x) :
-    HasStrictFderivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') x :=
-  (Complex.hasStrictDerivAt_exp (f x)).comp_hasStrictFderivAt x hf
-#align has_strict_fderiv_at.cexp HasStrictFderivAt.cexp
+theorem HasStrictFDerivAt.cexp (hf : HasStrictFDerivAt f f' x) :
+    HasStrictFDerivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') x :=
+  (Complex.hasStrictDerivAt_exp (f x)).comp_hasStrictFDerivAt x hf
+#align has_strict_fderiv_at.cexp HasStrictFDerivAt.cexp
 
-theorem HasFderivWithinAt.cexp (hf : HasFderivWithinAt f f' s x) :
-    HasFderivWithinAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') s x :=
-  (Complex.hasDerivAt_exp (f x)).comp_hasFderivWithinAt x hf
-#align has_fderiv_within_at.cexp HasFderivWithinAt.cexp
+theorem HasFDerivWithinAt.cexp (hf : HasFDerivWithinAt f f' s x) :
+    HasFDerivWithinAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') s x :=
+  (Complex.hasDerivAt_exp (f x)).comp_hasFDerivWithinAt x hf
+#align has_fderiv_within_at.cexp HasFDerivWithinAt.cexp
 
-theorem HasFderivAt.cexp (hf : HasFderivAt f f' x) :
-    HasFderivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') x :=
-  hasFderivWithinAt_univ.1 <| hf.HasFderivWithinAt.cexp
-#align has_fderiv_at.cexp HasFderivAt.cexp
+theorem HasFDerivAt.cexp (hf : HasFDerivAt f f' x) :
+    HasFDerivAt (fun x => Complex.exp (f x)) (Complex.exp (f x) • f') x :=
+  hasFDerivWithinAt_univ.1 <| hf.HasFDerivWithinAt.cexp
+#align has_fderiv_at.cexp HasFDerivAt.cexp
 
 theorem DifferentiableWithinAt.cexp (hf : DifferentiableWithinAt 𝕜 f s x) :
     DifferentiableWithinAt 𝕜 (fun x => Complex.exp (f x)) s x :=
-  hf.HasFderivWithinAt.cexp.DifferentiableWithinAt
+  hf.HasFDerivWithinAt.cexp.DifferentiableWithinAt
 #align differentiable_within_at.cexp DifferentiableWithinAt.cexp
 
 @[simp]
 theorem DifferentiableAt.cexp (hc : DifferentiableAt 𝕜 f x) :
     DifferentiableAt 𝕜 (fun x => Complex.exp (f x)) x :=
-  hc.HasFderivAt.cexp.DifferentiableAt
+  hc.HasFDerivAt.cexp.DifferentiableAt
 #align differentiable_at.cexp DifferentiableAt.cexp
 
 theorem DifferentiableOn.cexp (hc : DifferentiableOn 𝕜 f s) :
@@ -280,30 +280,30 @@ theorem ContDiffWithinAt.exp {n} (hf : ContDiffWithinAt ℝ n f s x) :
   Real.contDiff_exp.ContDiffAt.comp_contDiffWithinAt x hf
 #align cont_diff_within_at.exp ContDiffWithinAt.exp
 
-theorem HasFderivWithinAt.exp (hf : HasFderivWithinAt f f' s x) :
-    HasFderivWithinAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') s x :=
-  (Real.hasDerivAt_exp (f x)).comp_hasFderivWithinAt x hf
-#align has_fderiv_within_at.exp HasFderivWithinAt.exp
+theorem HasFDerivWithinAt.exp (hf : HasFDerivWithinAt f f' s x) :
+    HasFDerivWithinAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') s x :=
+  (Real.hasDerivAt_exp (f x)).comp_hasFDerivWithinAt x hf
+#align has_fderiv_within_at.exp HasFDerivWithinAt.exp
 
-theorem HasFderivAt.exp (hf : HasFderivAt f f' x) :
-    HasFderivAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') x :=
-  (Real.hasDerivAt_exp (f x)).comp_hasFderivAt x hf
-#align has_fderiv_at.exp HasFderivAt.exp
+theorem HasFDerivAt.exp (hf : HasFDerivAt f f' x) :
+    HasFDerivAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') x :=
+  (Real.hasDerivAt_exp (f x)).comp_hasFDerivAt x hf
+#align has_fderiv_at.exp HasFDerivAt.exp
 
-theorem HasStrictFderivAt.exp (hf : HasStrictFderivAt f f' x) :
-    HasStrictFderivAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') x :=
-  (Real.hasStrictDerivAt_exp (f x)).comp_hasStrictFderivAt x hf
-#align has_strict_fderiv_at.exp HasStrictFderivAt.exp
+theorem HasStrictFDerivAt.exp (hf : HasStrictFDerivAt f f' x) :
+    HasStrictFDerivAt (fun x => Real.exp (f x)) (Real.exp (f x) • f') x :=
+  (Real.hasStrictDerivAt_exp (f x)).comp_hasStrictFDerivAt x hf
+#align has_strict_fderiv_at.exp HasStrictFDerivAt.exp
 
 theorem DifferentiableWithinAt.exp (hf : DifferentiableWithinAt ℝ f s x) :
     DifferentiableWithinAt ℝ (fun x => Real.exp (f x)) s x :=
-  hf.HasFderivWithinAt.exp.DifferentiableWithinAt
+  hf.HasFDerivWithinAt.exp.DifferentiableWithinAt
 #align differentiable_within_at.exp DifferentiableWithinAt.exp
 
 @[simp]
 theorem DifferentiableAt.exp (hc : DifferentiableAt ℝ f x) :
     DifferentiableAt ℝ (fun x => Real.exp (f x)) x :=
-  hc.HasFderivAt.exp.DifferentiableAt
+  hc.HasFDerivAt.exp.DifferentiableAt
 #align differentiable_at.exp DifferentiableAt.exp
 
 theorem DifferentiableOn.exp (hc : DifferentiableOn ℝ f s) :
@@ -317,13 +317,13 @@ theorem Differentiable.exp (hc : Differentiable ℝ f) : Differentiable ℝ fun
 
 theorem fderivWithin_exp (hf : DifferentiableWithinAt ℝ f s x) (hxs : UniqueDiffWithinAt ℝ s x) :
     fderivWithin ℝ (fun x => Real.exp (f x)) s x = Real.exp (f x) • fderivWithin ℝ f s x :=
-  hf.HasFderivWithinAt.exp.fderivWithin hxs
+  hf.HasFDerivWithinAt.exp.fderivWithin hxs
 #align fderiv_within_exp fderivWithin_exp
 
 @[simp]
 theorem fderiv_exp (hc : DifferentiableAt ℝ f x) :
     fderiv ℝ (fun x => Real.exp (f x)) x = Real.exp (f x) • fderiv ℝ f x :=
-  hc.HasFderivAt.exp.fderiv
+  hc.HasFDerivAt.exp.fderiv
 #align fderiv_exp fderiv_exp
 
 end

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,13 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
 
 ! This file was ported from Lean 3 source module analysis.special_functions.exp_deriv
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Inverse
 import Mathbin.Analysis.Complex.RealDeriv
-import Mathbin.Analysis.SpecialFunctions.Exp
 
 /-!
 # Complex and real exponential

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -36,9 +36,9 @@ variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ]
 /-- The complex exponential is everywhere differentiable, with the derivative `exp x`. -/
 theorem hasDerivAt_exp (x : ℂ) : HasDerivAt exp (exp x) x :=
   by
-  rw [hasDerivAt_iff_isOCat_nhds_zero]
+  rw [hasDerivAt_iff_isLittleO_nhds_zero]
   have : (1 : ℕ) < 2 := by norm_num
-  refine' (is_O.of_bound ‖exp x‖ _).trans_isOCat (is_o_pow_id this)
+  refine' (is_O.of_bound ‖exp x‖ _).trans_isLittleO (is_o_pow_id this)
   filter_upwards [Metric.ball_mem_nhds (0 : ℂ) zero_lt_one]
   simp only [Metric.mem_ball, dist_zero_right, norm_pow]
   exact fun z hz => exp_bound_sq x z hz.le

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -63,7 +63,7 @@ theorem iter_deriv_exp : ∀ n : ℕ, deriv^[n] exp = exp
 
 theorem contDiff_exp : ∀ {n}, ContDiff 𝕜 n exp := by
   -- Porting note: added `@` due to `∀ {n}` weirdness above
-  refine' @(contDiff_all_iff_nat.2 fun n => ?_)
+  refine @(contDiff_all_iff_nat.2 fun n => ?_)
   have : ContDiff ℂ (↑n) exp := by
     induction' n with n ihn
     · exact contDiff_zero.2 continuous_exp

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
 -/
 import Mathlib.Analysis.Complex.RealDeriv
-import Mathlib.Analysis.Calculus.ContDiff.IsROrC
+import Mathlib.Analysis.Calculus.ContDiff.RCLike
 import Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas
 
 #align_import analysis.special_functions.exp_deriv from "leanprover-community/mathlib"@"6a5c85000ab93fe5dcfdf620676f614ba8e18c26"

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -62,7 +62,7 @@ theorem iter_deriv_exp : ∀ n : ℕ, deriv^[n] exp = exp
 #align complex.iter_deriv_exp Complex.iter_deriv_exp
 
 theorem contDiff_exp : ∀ {n}, ContDiff 𝕜 n exp := by
-  -- porting note: added `@` due to `∀ {n}` weirdness above
+  -- Porting note: added `@` due to `∀ {n}` weirdness above
   refine' @(contDiff_all_iff_nat.2 fun n => ?_)
   have : ContDiff ℂ (↑n) exp := by
     induction' n with n ihn

Based on @CBirkbeck's work on modular forms.

@@ -5,6 +5,7 @@ Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
 -/
 import Mathlib.Analysis.Complex.RealDeriv
 import Mathlib.Analysis.Calculus.ContDiff.IsROrC
+import Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas
 
 #align_import analysis.special_functions.exp_deriv from "leanprover-community/mathlib"@"6a5c85000ab93fe5dcfdf620676f614ba8e18c26"
 
@@ -25,6 +26,8 @@ open Filter Asymptotics Set Function
 
 open scoped Classical Topology
 
+/-! ## `Complex.exp` -/
+
 namespace Complex
 
 variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ]
@@ -174,6 +177,15 @@ theorem ContDiffWithinAt.cexp {n} (hf : ContDiffWithinAt 𝕜 n f s x) :
 
 end
 
+open Complex in
+@[simp]
+theorem iteratedDeriv_cexp_const_mul (n : ℕ) (c : ℂ) :
+    (iteratedDeriv n fun s : ℂ => exp (c * s)) = fun s => c ^ n * exp (c * s) := by
+  rw [iteratedDeriv_const_mul contDiff_exp, iteratedDeriv_eq_iterate, iter_deriv_exp]
+
+
+/-! ## `Real.exp` -/
+
 namespace Real
 
 variable {x y z : ℝ}
@@ -319,3 +331,9 @@ theorem fderiv_exp (hc : DifferentiableAt ℝ f x) :
 #align fderiv_exp fderiv_exp
 
 end
+
+open Real in
+@[simp]
+theorem iteratedDeriv_exp_const_mul (n : ℕ) (c : ℝ) :
+    (iteratedDeriv n fun s => exp (c * s)) = fun s => c ^ n * exp (c * s) := by
+  rw [iteratedDeriv_const_mul contDiff_exp, iteratedDeriv_eq_iterate, iter_deriv_exp]

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
 -/
 import Mathlib.Analysis.Complex.RealDeriv
+import Mathlib.Analysis.Calculus.ContDiff.IsROrC
 
 #align_import analysis.special_functions.exp_deriv from "leanprover-community/mathlib"@"6a5c85000ab93fe5dcfdf620676f614ba8e18c26"
 

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -26,7 +26,7 @@ open scoped Classical Topology
 
 namespace Complex
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ]
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ]
 
 /-- The complex exponential is everywhere differentiable, with the derivative `exp x`. -/
 theorem hasDerivAt_exp (x : ℂ) : HasDerivAt exp (exp x) x := by
@@ -81,7 +81,7 @@ end Complex
 
 section
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ] {f : 𝕜 → ℂ} {f' : ℂ} {x : 𝕜}
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ] {f : 𝕜 → ℂ} {f' : ℂ} {x : 𝕜}
   {s : Set 𝕜}
 
 theorem HasStrictDerivAt.cexp (hf : HasStrictDerivAt f f' x) :
@@ -114,7 +114,7 @@ end
 
 section
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ] {E : Type _}
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedAlgebra 𝕜 ℂ] {E : Type*}
   [NormedAddCommGroup E] [NormedSpace 𝕜 E] {f : E → ℂ} {f' : E →L[𝕜] ℂ} {x : E} {s : Set E}
 
 theorem HasStrictFDerivAt.cexp (hf : HasStrictFDerivAt f f' x) :
@@ -251,7 +251,7 @@ section
 function, for standalone use and use with `simp`. -/
 
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {f' : E →L[ℝ] ℝ} {x : E}
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] {f : E → ℝ} {f' : E →L[ℝ] ℝ} {x : E}
   {s : Set E}
 
 theorem ContDiff.exp {n} (hf : ContDiff ℝ n f) : ContDiff ℝ n fun x => Real.exp (f x) :=

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-
-! This file was ported from Lean 3 source module analysis.special_functions.exp_deriv
-! leanprover-community/mathlib commit 6a5c85000ab93fe5dcfdf620676f614ba8e18c26
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Complex.RealDeriv
 
+#align_import analysis.special_functions.exp_deriv from "leanprover-community/mathlib"@"6a5c85000ab93fe5dcfdf620676f614ba8e18c26"
+
 /-!
 # Complex and real exponential
 

@@ -55,7 +55,7 @@ theorem deriv_exp : deriv exp = exp :=
 #align complex.deriv_exp Complex.deriv_exp
 
 @[simp]
-theorem iter_deriv_exp : ∀ n : ℕ, (deriv^[n]) exp = exp
+theorem iter_deriv_exp : ∀ n : ℕ, deriv^[n] exp = exp
   | 0 => rfl
   | n + 1 => by rw [iterate_succ_apply, deriv_exp, iter_deriv_exp n]
 #align complex.iter_deriv_exp Complex.iter_deriv_exp
@@ -205,7 +205,7 @@ theorem deriv_exp : deriv exp = exp :=
 #align real.deriv_exp Real.deriv_exp
 
 @[simp]
-theorem iter_deriv_exp : ∀ n : ℕ, (deriv^[n]) exp = exp
+theorem iter_deriv_exp : ∀ n : ℕ, deriv^[n] exp = exp
   | 0 => rfl
   | n + 1 => by rw [iterate_succ_apply, deriv_exp, iter_deriv_exp n]
 #align real.iter_deriv_exp Real.iter_deriv_exp

This incorporates the changes from https://github.com/leanprover-community/mathlib/pull/19139 which haven't hit mathport yet due to mathport CI failing for a few days. (Hopefully it will succeed on the next run.)