求函数y=√[﹙﹙x-1﹚﹙x-2﹚∧2﹚/﹙3-x﹚]的导数,√是立方根
问题描述:
求函数y=√[﹙﹙x-1﹚﹙x-2﹚∧2﹚/﹙3-x﹚]的导数,√是立方根
答
先两边取对数
lny=(1/3)ln|x-1|+(2/3)ln|x-2|-(1/3)ln|3-x|
再两边求导得到
(1/y)(y的导数)=(1/3)(1/(x-1)+2/(x-2)+1/(x-3))
y的导数=(1/3)(1/(x-1)+2/(x-2)+1/(x-3))√[﹙﹙x-1﹚﹙x-2﹚∧2﹚/﹙3-x﹚