⑩天掌 Teaching Plan on Advanced Mathematics 例8设y=x2e2,求y20) 解设u=c 2x y x2,则 u (k) k 2x 2 (k=1,2,20) v'=2x,v"=2,v)=0k=3,4,…20 代入莱布尼茨公式,得 y2)=(2)2).x2+20(c2)0.(x2 20(20-1)n2x)(.2 (x2)"+0 0202 20·19 e4·x2+20·2e2x.2x+ 2 182x 2 2! =2e(x2+20x+95) 「返回 Tianjin Polytechnic Moiwendity wTianjin Polytechnic University Teaching Plan on Advanced Mathematics 例8 , . 2 2 (20) y x e y 设 = x 求 解 设u = e 2x ,v = x 2 ,则 2 , 2, 0( 3,4, 20), 2 ( ) ( ) 2  =  = = =  = v x v v k u e k k k x (k = 1,2, 20) 代入莱布尼茨公式,得 ( ) ( ) 0 2! 20(20 1) ( ) 20( ) ( ) 2 (18) 2 (20) 2 (20) 2 2 (19) 2   + − + =  +   e x y e x e x x x x 2 2 2! 20 19 2 20 2 2 20 2 2 19 2 18 2   =  +   + x x x e x e x e 2 ( 20 95) 20 2 2 = e x + x + x 返回