What is the derivative of \sqrt[9]{x^8} ?

The derivative of \sqrt[9]{x^8} is 8/(9x^{1/9)}

What is the first derivative of \sqrt[9]{x^8} ?

The first derivative of \sqrt[9]{x^8} is 8/(9x^{1/9)}

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\frac{8}{9 x ^{\frac{1}{9}}}

Solution steps

Apply the chain rule:

\frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \frac{d}{d x} (x^{8})

= \frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \cdot 8 x^{7}

Simplify

\frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \cdot 8 x^{7} : \frac{8}{9 x ^{\frac{1}{9}}}

= \frac{8}{9 x ^{\frac{1}{9}}}

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What is the derivative of \sqrt[9]{x^8} ?
The derivative of \sqrt[9]{x^8} is 8/(9x^{1/9)}
What is the first derivative of \sqrt[9]{x^8} ?
The first derivative of \sqrt[9]{x^8} is 8/(9x^{1/9)}