What is the derivative of 1/(\sqrt[3]{x}) ?

The derivative of 1/(\sqrt[3]{x}) is -1/(3x^{4/3)}

What is the first derivative of 1/(\sqrt[3]{x}) ?

The first derivative of 1/(\sqrt[3]{x}) is -1/(3x^{4/3)}

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- \frac{1}{3 x ^{\frac{4}{3}}}

Solution steps

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

- \frac{1}{3} x^{- \frac{1}{3} - 1} : - \frac{1}{3 x ^{\frac{4}{3}}}

= - \frac{1}{3 x ^{\frac{4}{3}}}

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What is the derivative of 1/(\sqrt[3]{x}) ?
The derivative of 1/(\sqrt[3]{x}) is -1/(3x^{4/3)}
What is the first derivative of 1/(\sqrt[3]{x}) ?
The first derivative of 1/(\sqrt[3]{x}) is -1/(3x^{4/3)}