怎样用乘积求导、复合函数求导公式证明商求导公式?

2025-05-05 05:08:57
推荐回答(1个)
回答(1):

[u(x)/v(x)]'
={u(x)·[1/v(x)]}'
(乘积求导)
=u(x)'·[1/v(x)]+u(x)·[1/v(x)]'
([1/v(x)]'用复合函数求导,f(x)=1/x,1/v(x)=f[v(x)])
=u(x)'·[1/v(x)]+u(x)·[v(x)']/[v(x)·v(x)]
(通分,分母变成[v(x)·v(x)])
=[u(x)'·v(x)+u(x)·v(x)']/[v(x)·v(x)]