已知y=ln[(x+1)/(x-1)],求dy/dx

来源：学生作业帮助网编辑：作业帮时间：2024/05/12 00:48:51

已知y=ln[(x+1)/(x-1)],求dy/dx
已知y=ln[(x+1)/(x-1)],求dy/dx

已知y=ln[(x+1)/(x-1)],求dy/dx
应该这样
y=ln[(x+1)/(x-1)]
=ln(x+1)-ln(x-1)
再求导,得
y'=1/(x+1)-1/(x-1)
=-2/(x+1)(x-1) （可以不写）

dy/dx=y'={1/[(x+1)/(x-1)]}×[(x+1)/(x-1)]'
=[(x-1)/(x+1)][(x+1)'(x-1)-(x+1)(x-1)']/(x-1)²
=[(x-1)/(x+1)](x-1-x-1)/(x-1)²
=[(x-1)/(x+1)][(-2)/(x-1)²]
=(-2)(x-1)/[(x-1)²(x+1)]
=-2/[(x-1)(x+1)]
=-2/(x²-1)

求导y=ln ln ln(x^2+1) 已知ln(x-y)+ln(x+2y)=ln2+ln(x)+ln(y),求x/y的值. 已知集合S={y/y=2^x},集合T={x/ln(x-1) 求导：y=(ln x)^x + x^(1/x) 函数y=ln(x-1)中ln的含义? 函数y=ln(ln(x-1))的定义域是? 常微分方程y'=(x+y)ln(x+y)-1 y=ln[ln(ln x)] 求导已知y=ln(x+√x∧2+1)arcsinx,求y' y=ln(2x^-1)求导 y=ln(1+x^2)求导 y=ln^2(1-x)求导求导：y=[ln(1-x)]^2 求导数 y=ln(1+x) y=3 ln(x +1)定义域 y=ln(x-1)的图像 y=1/ln(x-5) 定义域已知(ln√x)(lny)=1,其中x,y∈(1,正无穷),则ln(xy)的最小值为