证(3)设y=队u(x):v(x) Ay=u(x+ 4r) v(x+4c)-u(x).v(r) u(x+Ax)v(x+Ax)-u(xv(+4r) tu(x)v(x+4x)-u(x)v(x) =4n·(x+Ax)+u(x)·4v v(x+Ac)+u() ∠x∠v ∠x J=im分 A im[“(x+Ax)+u(x) 4x->0∠x4x-→04 Ax 可导必连续 L(x)·w(x)+Lx)卩(x 2021/2/202021/2/20 5 设y = u(x) v(x) = u(x + x)v(x + x) − u(x)v(x + x) = u v(x + x) + u(x)v + u(x)v(x + x) − u(x)v(x) [证] (3) x v v x x u x x u x y        =  ( + )+ ( ) ( ) ( ) ( ) ( ) lim lim [ ( ) ( ) ] 0 0 u x v x u x v x x v v x x u x x u x y y x x =   +    = =  + +  → →          可导必连续 y = u(x + x) v(x + x) − u(x) v(x)