求y=arccos(x+1⼀x-1)导数

过程
2025-05-05 22:43:09
推荐回答(2个)
回答1:

y=arccos(x+1)/(x-1)
y'=-1/√[1-((x+1)/(x-1))^2] * ((x+1)/(x-1))'
y'=2/√[1-((x+1)/(x-1))^2] * (1/(x-1)^2)
因为:1-((x+1)/(x-1))^2>0
(x-1)^2-(x+1)^2>0,即:-4x>0,x<0 x-1<0
y'=2/√[1-((x+1)/(x-1))^2] * (1/(x-1)^2)
=-2/[√(-4x)*(x-1)]

回答2:

令x+1/x-1=g(x)
就化为了复合函数求导、
y'=-1/根号下(1-g^2(x))乘以g(x)的导数