如果函数=(x)及=v(x)在点x具有导数,那么它们的和在 点x也具有导数,并且 Lu(x)tv(xl=u(x)+v(x) 证明由导数的定义, Lu(x)+v(x)=lim lu(x+h)+v(x+h)]-lu(x)tvx)] h→>0 h =n/(x+h)-(x)+(x+h)-v(x) h-y h uTv(X 上页 返回 下页上页 返回 下页 如果函数u=u(x)及v=v(x)在点x具有导数那么它们的和在 点x也具有导数 并且 [u(x)v(x)]=u(x)v(x) 证明 由导数的定义 =u(x)v(x) h u x h v x h u x v x u x v x h [ ( ) ( )] [ ( ) ( )] [ ( ) ( )] lim 0 +  + −    = →     + −  + − = → h v x h v x h u x h u x h ( ) ( ) ( ) ( ) lim 0 h u x h v x h u x v x u x v x h [ ( ) ( ) ] [ ( ) ( ) ] [ ( ) ( )] lim 0 +  + −    = →