Theorem dvcos

Description: Derivative of the cosine function. (Contributed by Mario Carneiro, 21-May-2016)

	Ref	Expression
Assertion	dvcos	⊢ ( ℂ D cos ) = ( 𝑥 ∈ ℂ ↦ - ( sin ‘ 𝑥 ) )

Proof

Step	Hyp	Ref	Expression
1		dvsincos	⊢ ( ( ℂ D sin ) = cos ∧ ( ℂ D cos ) = ( 𝑥 ∈ ℂ ↦ - ( sin ‘ 𝑥 ) ) )
2	1	simpri	⊢ ( ℂ D cos ) = ( 𝑥 ∈ ℂ ↦ - ( sin ‘ 𝑥 ) )