f(x)=(2x+3)/(x-1) 的导函数f(x)=(2x+3)/(x-1) 的反函数为

问题描述:

f(x)=(2x+3)/(x-1) 的导函数
f(x)=(2x+3)/(x-1) 的反函数为

f(x)=2+5/(x-1)
f'(x)=-5/(x-1)^2

f(x)=(2x+3)/(x-1)
=2+5/(x-1)
∴f'(x)=-5/(x-1)^2

f(x)=(2x+3)/(x-1)
f'(x)=[2(x-1) - (2x+3)] / (x-1)^2
=(2x-2-2x-3) / (x-1)^2
=-5/(x-1)^2

=-5/(x-1)²