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Popular >

derivative of \sqrt[3]{x}-6/x

Solution

Solution

\frac{x ^{2} + 18 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

Solution steps

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

\frac{d}{d x} (\frac{6}{x}) = - \frac{6}{x ^{2}}

= \frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{6}{x ^{2}})

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{6}{x ^{2}}) : \frac{x ^{2} + 18 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

= \frac{x ^{2} + 18 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{x}-6/x ?
The derivative of \sqrt[3]{x}-6/x is (x^2+18x^{2/3})/(3x^{8/3)}
What is the first derivative of \sqrt[3]{x}-6/x ?
The first derivative of \sqrt[3]{x}-6/x is (x^2+18x^{2/3})/(3x^{8/3)}