Differentiate and simplify: y=sqrt[5]{(ln x)^{4}}

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Accepted Answer

Step:1 ：Given the function (y=sqrt[5]{(ln x)^{4}})Step:2 ：We can rewrite the function as (y=(ln x)^{4/5})Step:3 ：Using the chain rule and the power rule, we differentiate the functionStep:4 ：The derivative of the function (y=(ln x)^{4/5}) is (0.8/(x*ln(x)^{0.2}))Step:5 ：(boxed{0.8/(x*ln(x)^{0.2})}) is the simplified form of the derivative

Answer

Step: 1 ：Given the function (y=sqrt[5]{(ln x)^{4}})Step: 2 ：We can rewrite the function as (y=(ln x)^{4/5})Step: 3 ：Using the chain rule and the power rule, we differentiate the functionStep: 4 ：The derivative of the function (y=(ln x)^{4/5}) is (0.8/(x*ln(x)^{0.2}))Step: 5 ：(boxed{0.8/(x*ln(x)^{0.2})}) is the simplified form of the derivative

Differentiate and simplify: $y=\sqrt[5]{(\ln x)^{4}}$

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