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Popular >

derivative of \sqrt[3]{8/x}

Solution

\frac{d}{d x} (3 \frac{8}{x})

Solution

- \frac{2}{3 x ^{\frac{4}{3}}}

Solution steps

\frac{d}{d x} (3 \frac{8}{x})

Apply the chain rule:

\frac{1}{3 ( \frac{8}{x} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{8}{x})

= \frac{1}{3 ( \frac{8}{x} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{8}{x})

\frac{d}{d x} (\frac{8}{x}) = - \frac{8}{x ^{2}}

= \frac{1}{3 ( \frac{8}{x} ) ^{\frac{2}{3}}} (- \frac{8}{x ^{2}})

Simplify

\frac{1}{3 ( \frac{8}{x} ) ^{\frac{2}{3}}} (- \frac{8}{x ^{2}}) : - \frac{2}{3 x ^{\frac{4}{3}}}

= - \frac{2}{3 x ^{\frac{4}{3}}}

Graph

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\int_{0}^{3} \frac{1}{x ^{2} + 9} d x

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{8/x} ?
The derivative of \sqrt[3]{8/x} is -2/(3x^{4/3)}
What is the first derivative of \sqrt[3]{8/x} ?
The first derivative of \sqrt[3]{8/x} is -2/(3x^{4/3)}