What is (\partial)/(\partial x)(\sqrt[3]{x^4}) ?

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

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(\partial)/(\partial x)(\sqrt[3]{x^4})

\frac{\partial}{\partial x} (3 x^{4})

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

Solution steps

\frac{\partial}{\partial x} (3 x^{4})

Apply the chain rule:

\frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \frac{\partial}{\partial x} (x^{4})

= \frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \frac{\partial}{\partial x} (x^{4})

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

= \frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \cdot 4 x^{3}

Simplify

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

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

\frac{d}{d x} ((\frac{x ^{3}}{x ^{8} + 9})^{2})

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\int \frac{12}{x ^{4}} d x

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