Theorems · Theorem · real analysis
Real.hasDerivAt_cos
∀ (x : ℝ), HasDerivAt Real.cos (-Real.sin x) x
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Complex.ofRealproof · cited by 1,654
- HasDerivAtstatement · cited by 493
- Real.cosstatement · cited by 424
- Real.sinstatement · cited by 389
- Complex.hasDerivAt_cosproof · cited by 10
- HasDerivAt.real_of_complexproof · cited by 7
Cited by12
Results whose statement or proof uses this declaration.
- integral_sin_pow_odd_mul_cos_powproof · cited by 3
- hasFDerivAt_polarCoord_symmproof · cited by 3
- HasFDerivAt.cosproof · cited by 2
- HasFDerivWithinAt.cosproof · cited by 2
- Real.differentiable_cosproof · cited by 2
- integral_cos_pow_auxproof · cited by 1
- integral_sin_pow_auxproof · cited by 1
- HasDerivAt.cosproof · cited by 1
- Real.deriv_cosproof · cited by 1
- EulerSine.integral_cos_mul_cos_pow_auxproof · cited by 1
- HasDerivWithinAt.cosproof · cited by 1
- integral_cos_sq_sub_sin_sqproof · cited by 0