导数4

一道用导数的定义求导的问题如何用

△y=f(x+△x)-f(x)=(x+△x)^(2/3)-x^(2/3) =[(x+△x)^(1/3)-x^(1/3)][(x+△x)^(1/3)+x^(1/3)] =△x*[(x+△x)^(1/3)+x^(1/3)]/[(x+△x)^(2/3)+(x+△x)^(1/3)*x^(1/3)+x^(2/3)] △y/△x=[(x+△x)^(1/3)+x^(1/3)]/[(x+△x)^(2/3)+(x+△x)^(1/3)*x^(1/3)+x^(2/3)] 令△x→0，有y'=[2*x^(1/3)]/[3*x^(2/3)]=(2/3)*x^(-1/3)。 。全部

  △y=f(x+△x)-f(x)=(x+△x)^(2/3)-x^(2/3) =[(x+△x)^(1/3)-x^(1/3)][(x+△x)^(1/3)+x^(1/3)] =△x*[(x+△x)^(1/3)+x^(1/3)]/[(x+△x)^(2/3)+(x+△x)^(1/3)*x^(1/3)+x^(2/3)] △y/△x=[(x+△x)^(1/3)+x^(1/3)]/[(x+△x)^(2/3)+(x+△x)^(1/3)*x^(1/3)+x^(2/3)] 令△x→0，有y'=[2*x^(1/3)]/[3*x^(2/3)]=(2/3)*x^(-1/3)。
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