用倒数定义求x^(2/3)导数,就是用{f(x+d)-f(x)}/d的方法求

由立方差公式△y＝(x+d)^(2/3)－x^(2/3)
＝[(x+d)^2-x^2]/[(x+d)^(4/3)＋(x^2+dx)^(2/3)＋x^(4/3)]
＝d(2x＋d)/[(x+d)^(4/3)＋(x^2+dx)^(2/3)＋x^(4/3)]
所以,△y/d＝(2x＋d)/[(x+d)^(4/3)＋(x^2+dx)^(2/3)＋x^(4/3)],当d→0时,极限是 2x/[x^(4/3)＋x^(4/3)＋x^(4/3)]＝2/3×x^(-1/3)
所以,x^(2/3)的导数是2/3×x^(-1/3).