Theorems · Theorem · real analysis
HasStrictFDerivAt.const_rpow
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {x : E}
{c : ℝ}, HasStrictFDerivAt f f' x → 0 < c → HasStrictFDerivAt (fun x => c ^ f x) ((c ^ f x * Real.log c) • f') x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- 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
- HasStrictFDerivAtstatement and proof · cited by 261
- HasStrictDerivAt.comp_hasStrictFDerivAtproof · cited by 19
- Real.hasStrictDerivAt_const_rpowproof · cited by 3
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