( 2 sin x cos x )` = ( 2 sin x )` cos x + 2 sin x ( cos x )` =
= 2 cos x cos x + 2 sin x *( - sin x ) =
= 2 cos² x - 2 sin² x = 2 ( cos² x - sin² x ) = 2 cos ( 2 x )
Another way ( using trigonometric identities first ):
2 sin x cos x = sin ( 2 x )
( sin ( 2 x ) )` = 2 cos ( 2 x )
