What is the derivative of ln(\sqrt[3]{x^3+8}) ?

The derivative of ln(\sqrt[3]{x^3+8}) is (x^2)/(\sqrt[3]{x^3+8)(x^3+8)^{2/3}}

What is the first derivative of ln(\sqrt[3]{x^3+8}) ?

The first derivative of ln(\sqrt[3]{x^3+8}) is (x^2)/(\sqrt[3]{x^3+8)(x^3+8)^{2/3}}

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Solution steps

Apply the chain rule:

Simplify

What is the derivative of ln(\sqrt[3]{x^3+8}) ?
The derivative of ln(\sqrt[3]{x^3+8}) is (x^2)/(\sqrt[3]{x^3+8)(x^3+8)^{2/3}}
What is the first derivative of ln(\sqrt[3]{x^3+8}) ?
The first derivative of ln(\sqrt[3]{x^3+8}) is (x^2)/(\sqrt[3]{x^3+8)(x^3+8)^{2/3}}