[(x+2)/（x^2-4)]^1/3的导数

来源：百度知道编辑：UC知道时间：2024/06/08 07:20:41

[(x+2)/（x^2-4)]^1/3
=[1/(x-2)]^1/3
=(x-2)^(-1/3)

[(x+2)/（x^2-4)]^1/3的导数
=(x-2)^(-1/3)的导数
=(-1/3)(x-2)^(-4/3)*(x-2)'
=(-1/3)(x-2)^(-4/3)

{[(x+2)/（x^2-4)]^1/3}'
=1/3{[(x+2)/（x^2-4)]^(1/3-1)*{[(x+2)/（x^2-4)]'
=1/3[(x+2)/（x^2-4)]^(-2/3)*{(x+2)'(x^2-4)-(x+2)(x^2-4)'}/(x^2-4)^2
=1/3[(x+2)/（x^2-4)]^(-2/3)*[x^2-4-2x(x+2)]/(x^2-4)^2
=1/3[(x+2)/（x^2-4)]^(-2/3)*[x^2-2x^2-4x]/(x^2-4)^2
=1/3[(x+2)/（x^2-4)]^(-2/3)*[-x^2-4x]/(x^2-4)^2
=-1/3(x+2)^(-2/3)*(x^2+4x)/[x^2-4]^4/3

1/3(1/(x-2))^-2/3*-1/(x-2)^2

原式化简为(x-2)^1/3==1/3(x-2)^(-2/3)

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