x-a=[x^(1/3)-a^(1/3)][x^(2/3)+x^(1/3)a^(1/3)+a^(2/3)]所以f'(a)=lim(x趋于a)(f(x)-f(a))/x-a=lim(x趋于a)1/[x^(2/3)+x^(1/3)a^(1/3)+a^(2/3)]=1/(3*a^(2/3))=1/2*a^(-2/3)