y=x+(x-1)arcsin(x/1+x)^(1/2),求f'(x)
问题描述：
y=x+(x-1)arcsin(x/1+x)^(1/2),求f'(x)
答
y'=1+arcsin(x/1+x)^(1/2)+(x-1)[arcsin(x/1+x)^(1/2)]'=1+arcsin(x/1+x)^(1/2)+(x-1)/[1-(x/1+x)] / [2*(x/1+x)^1/2] / (1+x)^2=1+arcsin(x/1+x)^(1/2)+(x-1)/[2(x(1+x))^1/2]