What is (\partial)/(\partial x)(1/(\sqrt[3]{x)}) ?

The answer to (\partial)/(\partial x)(1/(\sqrt[3]{x)}) is -1/(3x^{4/3)}

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(\partial)/(\partial x)(1/(\sqrt[3]{x)})

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

Solution steps

Apply exponent rule:

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

= \frac{\partial}{\partial 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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f (x) = 8 arcsin (x^{4})

What is (\partial)/(\partial x)(1/(\sqrt[3]{x)}) ?
The answer to (\partial)/(\partial x)(1/(\sqrt[3]{x)}) is -1/(3x^{4/3)}