y=x+(x-1)arcsin(x/1+x)^(1/2),求f'(x)

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y=x+(x-1)arcsin(x/1+x)^(1/2),求f'(x)

y=x+(x-1)arcsin(x/1+x)^(1/2),求f'(x)
y=x+(x-1)arcsin(x/1+x)^(1/2),求f'(x)

y=x+(x-1)arcsin(x/1+x)^(1/2),求f'(x)
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]