函数求导 y=x+1/x-1 @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

根据公式
f(x)=g(x)*h(x)
f'(x)=g'(x)h(x)+g(x)h'(x)
y=(x+1)/(x-1)
=(x+1)*(x-1)^(-1)
y'=1*(x-1)^(-1)+(x+1)*(-1)*(x-1)^(-2)*1
=1/(x-1)-(x+1)/[(x-1)^2]
=(x-1)/[(x-1)^2]-(x+1)/[(x-1)^2]
=(x-1-x-1)/[(x-1)^2]
=-2/[(x-1)^2]