根号1+x平方=(1+x^2)^(1/2) y'=1/[x+(1+x^2)^(1/2)]*[1+(1/2)*1/(1+x^2)^(1/2)*2x] =[1+x/(1+x^2)^(1/2)]/[x+(1+x^2)^(1/2)] 分子分母同乘(1+x^2)^(1/2)得：y'=[(1+x^2)^(1/2)+x]/{[x+(1+x^2)^(1/2)]*(1+x^2)^(1/2)} 约分得：y'=1/(1+x^2)^(1/2)