Theorems · Theorem · real analysis
HasDerivWithinAt.const_rpow
∀ {f : ℝ → ℝ} {f' x : ℝ} {s : Set ℝ} {a : ℝ},
0 < a → HasDerivWithinAt f f' s x → HasDerivWithinAt (fun x => a ^ f x) (Real.log a * f' * a ^ f x) s x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldproof · cited by 8,742
- Nat.cast_zeroproof · cited by 1,870
- ContinuousSMulproof · cited by 1,016
- Real.logstatement and proof · cited by 939
- HasDerivWithinAtstatement and proof · cited by 333
- hasDerivWithinAt_constproof · cited by 13
- HasDerivWithinAt.rpowproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- HasDerivAt.const_rpowproof · cited by 1
- derivWithin_const_rpowproof · cited by 0