例4.求下列导数：（①(x“);(2)(x);(3)(shx)'. 解：(I)(x“y=(#nx)=en(ulnx)=x. =4x-1 (2)(x)=(e*In*)=e*In*.(xlnx)=x*(Inx+1) )y-(e)==hx 2 说明：类似可得 (chx)'=shx;(thx)'= ch2x (a*)'=axIna. shx= ex-e x shx thx= ax exlna 2 chx ooo⑧例4. 求下列导数: 解: (1) ( ) ( ) ln  =  x x e   ( ln x) x   −1 =   x ( ) ( ) ln  =  x x x x e (xln x) x (2) = x (ln x +1) (3) ( ) −   = − 2 (sh ) x x e e x 2 = x e x e − + = ch x 说明: 类似可得 (ch x) = sh x ; x x a a e ln = (th x) ( ) x a x x x ch sh th = 2 sh x x e e x − − = ; ch 1 2 x = a ln a . x = 机动 目录 上页 下页 返回 结束