Theorems · Theorem · real analysis
DifferentiableAt.log
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {x : E},
DifferentiableAt ℝ f x → f x ≠ 0 → DifferentiableAt ℝ (fun x => Real.log (f x)) x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Real.logstatement · cited by 939
- DifferentiableAtstatement and proof · cited by 617
- DifferentiableAt.hasFDerivAtproof · cited by 134
- HasFDerivAt.differentiableAtproof · cited by 83
- HasFDerivAt.logproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- Real.differentiableAt_binEntropyproof · cited by 4
- Real.deriv2_qaryEntropyproof · cited by 2
- Real.deriv_Gamma_natproof · cited by 2
- Chebyshev.primeCounting_eq_theta_div_log_add_integralproof · cited by 2
- Real.differentiableAt_binEntropy_iff_ne_zero_oneproof · cited by 1
- log_riemannZeta_add_log_sub_isBigO_ofRealproof · cited by 1
- Real.differentiableAt_inv_logproof · cited by 1
- Real.differentiableAt_log_logproof · cited by 1
- Differentiable.logproof · cited by 0
- Chebyshev.theta_eq_primeCounting_mul_log_sub_integralproof · cited by 0