)(u±v)'=±v 证:设f(x)=u(x)士v(x),则 f(x)=lim f(x+h)-f(x) h>0 h lim [u(x+h)士v(x+h)]-[u(x)±v(x)] h-→0 h lim (x+h)-u(x) ±lim (x+h)-v(x) h-→0 h h-→0 h =u'(x)±v'(x) 故结论成立 此法侧可推广到任意有限项的情形.例如, 例如,(u+v-w)}'=1+v'-w此法则可推广到任意有限项的情形. 证: 设 , 则 (1) (u v) = u v f (x) = u(x) v(x) h f x h f x f x h ( ) ( ) ( ) lim 0 + − = → h u x h v x h u x v x h [ ( ) ( )] [ ( ) ( )] lim 0 + + − = → h u x h u x h ( ) ( ) lim 0 + − = → h v x h v x h ( ) ( ) lim 0 + − → = u (x) v (x) 故结论成立. 机动 目录 上页 下页 返回 结束 例如