根据导数定义,求函数y=x^(2/3)的导数.?
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由立方差公式,
△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)
,6,
△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)
,6,
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