`BookProof.ChapterSoftmaxFluctuation.hasDerivAt_exp_mul` (beta c : ℝ) : HasDerivAt (fun b : ℝ => Real.exp (b * c)) (c * Real.exp (beta * c)) beta

Proved

BookProof.ChapterSoftmaxFluctuation.hasDerivAt_exp_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxFluctuation.

BookProof.ChapterSoftmaxFluctuation.hasDerivAt_exp_mul (beta c : ℝ) : HasDerivAt (fun b : ℝ => Real.exp (b * c)) (c * Real.exp (beta * c)) beta

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxFluctuation.hasDerivAt_exp_mul.

Preamble

-- Generated from ChapterSoftmaxFluctuation.lean — theorem BookProof.ChapterSoftmaxFluctuation.hasDerivAt_exp_mul
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSoftmaxFluctuation
open BookProof.ChapterSoftmaxFluctuation


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxFluctuation.hasDerivAt_exp_mul (beta c : ℝ) :
    HasDerivAt (fun b : ℝ => Real.exp (b * c)) (c * Real.exp (beta * c)) beta := by sorry

View graph