14)(sin x )'=cos x= sin(x+ (sin x)=sin(x+ D—2π-2 DI= cos(x +=sin(x+2 2 (sin x)=sin(x+3.2 2 inx)}=sin(x+n·).同理可证(cosx))=cos(x+n 例13已知(x)存在,且(x)≠0,y=(x,求 d 解中f(x) d y f"(x)f(x)-f(x) dx f(x) d x2 f2(x)5 (4) (sin ) cos sin( ) 2 x x x   = = + 例13 .已知 2 2 ( ) ( ) 0, ln[ ( )], . d y f x f x y f x dx  存 在，且  = 求 (sin ) sin( 3 ), 2 x x   = +  (sin ) [sin( )] cos( ) sin( 2 ) 2 2 2 x x x x      = + = + = +  ( ) (cos ) cos( ). 2 n x x n  同 理 可 证 = +  ( ) (sin ) sin( ). 2 n x x n  = +  ( ) ( ) dy f x dx f x 解 =  2 2 2 2 ( ) ( ) [ ( )] . ( ) d y f x f x f x dx f x   − =