Theorems · Theorem · real analysis
HasDerivAt.const_mul
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {d : 𝕜 → 𝔸} {d' : 𝔸} (c : 𝔸),
HasDerivAt d d' x → HasDerivAt (fun y => c * d y) (c * d') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- HasDerivAtstatement and proof · cited by 493
- hasDerivWithinAt_univproof · cited by 18
- HasDerivWithinAt.const_mulproof · cited by 6
Cited by25
Results whose statement or proof uses this declaration.
- ProbabilityTheory.gaussianReal_map_const_mulproof · cited by 4
- exists_ratio_hasDerivAt_eq_ratio_slopeproof · cited by 3
- hasDerivAt_circleMapproof · cited by 3
- ProbabilityTheory.hasDerivAt_integral_pow_mul_expproof · cited by 3
- UpperHalfPlane.hasDerivAt_denom_zpowproof · cited by 2
- hasDerivAt_ofReal_cpow_constproof · cited by 2
- Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_rangeproof · cited by 2
- exists_ratio_hasDerivAt_eq_ratio_slope'proof · cited by 2
- integral_exp_mul_complexproof · cited by 2
- exp_neg_integrableOn_Ioiproof · cited by 2
- deriv2_sqrt_mul_logproof · cited by 1
- deriv_const_mulproof · cited by 1