设y=(x-2)²/(1-2x)(1+x)整体开三次根,求dy

Question

如题所述

Answer 1

基本思路：

本题y为x的函数，求解y的微分dy时，先求y关于x的导数，再在后面乘上x的微分dx，所以微分dy=y'dx。

解答过程：

求导过程

所以y的微分dy为：

y的微分

Answer 2

y = [(x-2)²/(1-2x)(1+x)]^(1/3)
lny = (2/3)ln|x-2| - (1/3)ln|1-2x| - (1/3)ln|1+x|
y'/y = (2/3)/(x-2) + (2/3)/(1-2x) - (1/3)/(1+x)
y' = [(x-2)²/(1-2x)(1+x)]^(1/3)[(2/3)/(x-2) + (2/3)/(1-2x) - (1/3)/(1+x)]
dy = [(x-2)²/(1-2x)(1+x)]^(1/3)[(2/3)/(x-2) + (2/3)/(1-2x) - (1/3)/(1+x)]dx