Theorems · Theorem · real analysis
HasDerivAt.mul
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {c d : 𝕜 → 𝔸} {c' d' : 𝔸},
HasDerivAt c c' x → HasDerivAt d d' x → HasDerivAt (c * d) (c' * d x + c x * d') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 184 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.mulproof · cited by 7
Cited by20
Results whose statement or proof uses this declaration.
- deriv_fun_mulproof · cited by 15
- QuadraticMap.hasLineDerivAtproof · cited by 2
- norm_image_sub_le_of_norm_deriv_right_le_segmentproof · cited by 2
- expNegInvGlue.hasDerivAt_polynomial_eval_inv_mulproof · cited by 2
- deriv_mulproof · cited by 2
- MeasureTheory.integral_Ioi_deriv_mul_eq_subproof · cited by 1
- LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDerivproof · cited by 1
- AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_subproof · cited by 1
- Complex.partialGamma_add_oneproof · cited by 1
- Real.hasDerivAt_mulExpNegMulSqproof · cited by 1
- hasDerivAt_sqrt_mul_logproof · cited by 1
- Derivative.normalizedDerivOfComplex_slashproof · cited by 1