`BookProof.ChapterSoftmaxJacobian.hasDerivAt_exp_score` (beta t₀ : ℝ) (c : ℝ) : HasDerivAt (fun t : ℝ => Real.exp (beta * (c + t))) (beta * Real.exp (beta * (c + t₀))) t₀

Proved

BookProof.ChapterSoftmaxJacobian.hasDerivAt_exp_score

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxJacobian.

BookProof.ChapterSoftmaxJacobian.hasDerivAt_exp_score (beta t₀ : ℝ) (c : ℝ) : HasDerivAt (fun t : ℝ => Real.exp (beta * (c + t))) (beta * Real.exp (beta * (c + t₀))) t₀

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxJacobian.hasDerivAt_exp_score.

Preamble

-- Generated from ChapterSoftmaxJacobian.lean — theorem BookProof.ChapterSoftmaxJacobian.hasDerivAt_exp_score
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxJacobian
open BookProof.ChapterSoftmaxJacobian


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxJacobian.hasDerivAt_exp_score (beta t₀ : ℝ) (c : ℝ) :
    HasDerivAt (fun t : ℝ => Real.exp (beta * (c + t)))
      (beta * Real.exp (beta * (c + t₀))) t₀ := by sorry

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