Theorems · Theorem · real analysis
Real.deriv_rpow_const
∀ (x p : ℝ), deriv (fun x => x ^ p) x = p * x ^ (p - 1)
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MulZeroClass.zero_mulproof · cited by 1,625
- derivstatement and proof · cited by 676
- DifferentiableAtproof · cited by 617
- zero_subproof · cited by 335
- HasDerivAt.derivproof · cited by 147
- Real.rpow_zeroproof · cited by 69
- deriv_zero_of_not_differentiableAtproof · cited by 34
- deriv_const'proof · cited by 28
- Real.hasDerivAt_rpow_constproof · cited by 11
- Real.not_differentiableAt_rpow_const_zeroproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Real.deriv_rpow_const'proof · cited by 2
- AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFnproof · cited by 1
- AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFnproof · cited by 1
- deriv_norm_ofReal_cpowproof · cited by 1
- Real.iter_deriv_rpow_constproof · cited by 1