根据导数定义,求函数y＝x^(2/3)的导数.

△y＝(x+h)^(2/3)－x^(2/3)

＝[(x+h)^2-x^2]/[(x+h)^(4/3)＋(x^2+hx)^(2/3)＋x^(4/3)]

＝h(2x＋h)/[(x+h)^(4/3)＋(x^2+hx)^(2/3)＋x^(4/3)]

所以,

△y/h＝(2x＋h)/[(x+h)^(4/3)＋(x^2+hx)^(2/3)＋x^(4/3)],

当h→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)