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Theorems · Theorem · real analysis

HasDerivAt.inv

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝕜' : Type u_1} [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {c : 𝕜 → 𝕜'} {c' : 𝕜'}, HasDerivAt c c' x → c x ≠ 0 → HasDerivAt c⁻¹ (-c' / c x ^ 2) x
Defined in
Mathlib.Analysis.Calculus.Deriv.Inv
Cited by
5 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

deriv_fun_inv'' · cited by 3deriv_fun_inv''Real.hasDerivAt_sigmoid · cited by 1Real.hasDerivAt_sigmoidHasDerivAt.fun_inv · cited by 0HasDerivAt.fun_invderiv_riemannZeta_zero · cited by 0deriv_riemannZeta_zeroderiv_inv'' · cited by 0deriv_inv''NontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraHasDerivAt · cited by 493HasDerivAthasDerivWithinAt_univ · cited by 18hasDerivWithinAt_univHasDerivWithinAt.inv · cited by 3HasDerivWithinAt.invHasDerivAt.invCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.