Theorems · Theorem · real analysis
HasFDerivWithinAt.const_rpow
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {x : E}
{s : Set E} {c : ℝ},
HasFDerivWithinAt f f' s x → 0 < c → HasFDerivWithinAt (fun x => c ^ f x) ((c ^ f x * Real.log c) • f') s x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Real.logstatement · cited by 939
- StrongDualstatement and proof · cited by 459
- HasFDerivWithinAtstatement and proof · cited by 356
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- HasDerivAt.comp_hasFDerivWithinAtproof · cited by 22
- Real.hasStrictDerivAt_const_rpowproof · cited by 3
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