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Theorems · Theorem · real analysis

deriv_add

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {x : 𝕜},
  DifferentiableAt 𝕜 f x → DifferentiableAt 𝕜 g x → deriv (f + g) x = deriv f x + deriv g x
Defined in
Mathlib.Analysis.Calculus.Deriv.Add
Cited by
2 results in Mathlib
Foundations
Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

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

Real.deriv_Gamma_nat · cited by 2Real.deriv_Gamma_natDerivative.normalizedDerivOfComplex_add · cited by 1Derivative.normalizedDeri…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldderiv · cited by 676derivDifferentiableAt · cited by 617DifferentiableAtHasDerivAt.deriv · cited by 147HasDerivAt.derivDifferentiableAt.hasDerivAt · cited by 114DifferentiableAt.hasDeriv…HasDerivAt.add · cited by 13HasDerivAt.addderiv_addCITED BYCITES

Cites8

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Cited by2

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