首先:d(1/x)=(1/x)'dx=(-1/x²)dx 1¹²³
于是,d(1/x')=(1/x')'d(x')=[-1/(x')²]d(x') (考虑u=x',换元)
则原式=[-1/(x')²]*[d(x')/dy]*[1/(x')]
=[-1/(x')³]*x''
不就是1/u型式子直接求导么?
d(1/x')/dy = -1/(x')^2 dx'/dy = -x''/(x')^2
对y求导,详情如图所示
有任何疑惑,欢迎追问