Theorems · Theorem · real analysis
Complex.hasStrictDerivAt_cos
∀ (x : ℂ), HasStrictDerivAt Complex.cos (-Complex.sin x) x
The complex cosine function is everywhere strictly differentiable, with the derivative
-sin x.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Nat.cast_oneproof · cited by 2,501
- ContinuousSMulproof · cited by 1,016
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- div_eq_mul_invproof · cited by 715
- Complex.expproof · cited by 612
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
Cited by5
Results whose statement or proof uses this declaration.
- Complex.hasDerivAt_cosproof · cited by 10
- Real.hasStrictDerivAt_cosproof · cited by 2
- Complex.hasStrictDerivAt_tanproof · cited by 2
- HasStrictDerivAt.ccosproof · cited by 0
- HasStrictFDerivAt.ccosproof · cited by 0