例6求正弦函数和余弦函数的n阶导数 解y=sinx, y=cosx=sin(x+2), y=cos(x+/)=sin(x+2+2)=sin(x+2.) ,"=cOS(x+2. )=sin(x+2.+ 2 2=sIn(x+.T 般地,可得 yn)=sin(x+nA), Ep(sin x)(n)=sin(x+n. 用类似方法,可得(cosx))=cos(x+n-x) 页返回 页结束铃首页 上页 返回 下页 结束 铃 例6 求正弦函数和余弦函数的n阶导数 解 y=sin x 一般地 可得 ) 2 cos sin(  y  = x = x+  ) 2 ) sin( 2 2 2 ) sin( 2 cos(     y  = x+ = x+ + = x+   ) 2 ) sin( 3 2 2 ) sin( 2 2 cos( 2     y  = x+  = x+  + = x+   ) 2 sin( ( )  y = x+n n  即 ) 2 (sin ) sin( ( )  x = x+n n  用类似方法 可得 ) 2 (cos ) cos( ( )  x = x+n n  ) 2 cos sin(  y  = x = x+  ) 2 ) sin( 2 2 2 ) sin( 2 cos(     y  = x+ = x+ + = x+  ) 2 ) sin( 2 2 2 ) sin( 2 cos(     y  = x+ = x+ + = x+   ) 2 ) sin( 3 2 2 ) sin( 2 2 cos( 2     y  = x+  = x+  + = x+  )  2 ) sin( 3 2 2 ) sin( 2 2 cos( 2     y  = x+  = x+  + = x+   ) 2 sin( ( )  y = x+n n  即 ) 2 (sin ) sin( ( )  x = x+n n  下页