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Popular >

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

Solution

Solution

\frac{x ^{2} - 9 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{3}{x}) = - \frac{3}{x ^{2}}

= \frac{1}{3 x ^{\frac{2}{3}}} - \frac{3}{x ^{2}}

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} - \frac{3}{x ^{2}} : \frac{x ^{2} - 9 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

= \frac{x ^{2} - 9 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

Popular Examples

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\int e^{8 x} sin (x) d x

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{x}+3/x ?
The derivative of \sqrt[3]{x}+3/x is (x^2-9x^{2/3})/(3x^{8/3)}
What is the first derivative of \sqrt[3]{x}+3/x ?
The first derivative of \sqrt[3]{x}+3/x is (x^2-9x^{2/3})/(3x^{8/3)}