(3)/(r) u(xvey-u(xv(x (v(x)≠0) v(x 1(x 证(3)设f(x) ulr ,(v(x)≠0), f(r)=lim/(x+h)-f(r) h→0 u(x+h u(r) vr+ h) v(x) h→>0 lim u(x+ h)v(x)=u(x)v(x+h) h→>0 (x+ hv(x)h lim u(x+h)v(x)+u(x)v(x)=u(xv(x)u(x)v(x+h) h→>0 v(x+h)v(xh证(3) , ( ( ) 0), ( ) ( ) ( ) = v x  v x u x 设 f x h f x h f x f x h ( ) ( ) ( ) lim 0 + −  = → v x h v x h u x h v x u x v x h h ( ) ( ) ( ) ( ) ( ) ( ) lim 0 + + − + = → h v x u x v x h u x h h ( ) ( ) ( ) ( ) lim 0 − + + = → v x h v x h u x h v x u x v x u x v x u x v x h h ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) lim 0 + + + − − + = → ( ( ) 0). ( ) ( ) ( ) ( ) ( ) ] ( ) ( ) (3)[ 2   −   = v x v x u x v x u x v x v x u x