Theorems · Theorem · real analysis
deriv_update
∀ {𝕜 : Type u_1} {ι : Type u_2} [inst : DecidableEq ι] [inst_1 : NontriviallyNormedField 𝕜] [Finite ι] (x : ι → 𝕜)
(i : ι) (y : 𝕜), deriv (Function.update x i) y = Pi.single i 1- Defined in
- Mathlib.Analysis.Calculus.Deriv.Pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- derivstatement · cited by 676
- Pi.singlestatement · cited by 518
- Function.updatestatement · cited by 502
- Fintype.ofFiniteproof · cited by 255
- HasDerivAt.derivproof · cited by 147
- hasDerivAt_updateproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_auxproof · cited by 1
- deriv_singleproof · cited by 0