hasDerivAt_deriv_iff — Mathlib

English

The derivative within f s x, viewed as a linear map, applied to 1 equals the derivative within f s x.

Русский

Производная внутри f regarding s в x, применённая к единице, равна derivWithin f s x.

LaTeX

$$$f\text{derivWithin } 𝕜\; f\; s\; x\; (1) = \text{derivWithin } f\; s\; x$$$

Lean4

@[simp]
theorem hasDerivAt_deriv_iff : HasDerivAt f (deriv f x) x ↔ DifferentiableAt 𝕜 f x :=
  ⟨fun h => h.differentiableAt, fun h => h.hasDerivAt⟩

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