关键利用立方差公式a^3-b^3=(a-b)(a^2+ab+b^2),这里a=(x+h)^(1/3),b=x^1/3
具体证明如下
△y/h=[(x+h)^(1/3)-x^(1/3)]/h
=1/[(x+h)^(2/3)+(x+h)^(1/3) x^(1/3)+x^(2/3)]
(h→0）lim(△y/h)=1/[3x^(2/3)]=1/3*x^(-2/3)