嗯，对，是少了那项
y'=1/2*[x+√(x+√x)]^(-1/2)*［1+1/(2*√(x+√x))(1+1/2√x)］
=1/2*[x+√(x+√x)]^(-1/2)*［(1+2√(x+√x)]/2*√(x+√x)*(1+2√x)/2√x
=1/8* 1/［√x*√(x+√x)*(x+√(x+√x))] *［1+2√x+2√(x+√x)+4√x*√(x+√x)］
我帮你做一遍
y^2=x+√(x+√x)
y^2-x=√(x+√x)
y^4-2xy^2+x^2=x+√x
等式两边对x求导
4y^3*y'-2y^2-4xy*y'+2x=1+1/2√x
(4y^3-4xy)*y'=2y^2-2x+1+1/2√x
y'=(4√x*y^2-4x√x+2√x+1)/(8√x*y^3-8xy√x)
={4√x*[x+√(x+√x)]-4x√x+2√x+1}/{8√x*y*(y^2-x)
=[1+2√x+4√x*√(x+√x)]/{8√x*√[x+√(x+√x)]*√(x+√x)}
所以你给出的答案是正确的
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