返回上页 下页返回如果函数 u?u(x)及 v?v(x)在点 x具有导数?那么它们的积在点 x也具有导数?并且
[u(x)?v(x)]u?(x)v(x)?u(x)v?(x)?
h
xvxuhxvhxuxvxu
h
)()()()(lim])()([
0
)]()()()()()()()([1l i m 0 xvxuhxvxuhxvxuhxvhxuhh
h
xvhxvxuhxv
h
xuhxu
h
)()()()()()(lim
0
h
xvhxvxuhxv
h
xuhxu
hhh
)()(lim)()(lim)()(lim
000
u?(x)v(x)?u(x)v?(x)?
证明 由导数的定义?
[u(x)?v(x)]u?(x)v(x)?u(x)v?(x)?
h
xvxuhxvhxuxvxu
h
)()()()(lim])()([
0
)]()()()()()()()([1l i m 0 xvxuhxvxuhxvxuhxvhxuhh
h
xvhxvxuhxv
h
xuhxu
h
)()()()()()(lim
0
h
xvhxvxuhxv
h
xuhxu
hhh
)()(lim)()(lim)()(lim
000
u?(x)v(x)?u(x)v?(x)?
证明 由导数的定义?