Theorems · Theorem · global analysis
gradient_eq_deriv
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {g : 𝕜 → 𝕜} {u : 𝕜}, gradient g u = (starRingEnd 𝕜) (deriv g u)- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- RCLikestatement and proof · cited by 2,829
- map_zeroproof · cited by 1,614
- derivstatement and proof · cited by 676
- starRingEndstatement and proof · cited by 671
- DifferentiableAtproof · cited by 617
- HasDerivAt.derivproof · cited by 147
- deriv_zero_of_not_differentiableAtproof · cited by 34
- gradientstatement and proof · cited by 19
- HasGradientAt.hasDerivAtproof · cited by 2
- DifferentiableAt.hasGradientAtproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- gradient_eq_deriv'proof · cited by 0