Question

请问~~ (1-x)^(1/x) 的导数怎么求 给个过程~谢谢！

Answer 1

令f(x)= (1-x)^(1/x)
则lnf(x)=ln(1-x)/x
f`(x)/f(x)=-1/x(1-x)-ln(1-x)/x^2
f`(x)=(-1/x(1-x)-ln(1-x)/x^2) (1-x)^(1/x)

Answer 2

y=(1-x)^(1/x)
lny = (1/x)ln(1-x)
(1/y)y' = -1/[x(1-x)] - ln(1-x)/x^2
y' = -[1/[x(1-x)] + ln(1-x)/x^2] .(1-x)^(1/x)

追问

谢谢啦~