例6求正弦函数和余弦函数的n阶导数 解y=sinx y=cosx=sin(x+n) y=coS(x+n)=sin(x+n+A=sin(x+2 y=cos(x+2.7 2 )=sin(x+2+)=Sin(x+3.), 般地,可得 y)=si(x+n·x),即(sinx))=si(x+n·x) 用类似方法,可得(cosx)m)=cos(x+n 首页上页返回 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