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Popular >

derivative of \sqrt[3]{x^8}

Solution

\frac{d}{d x} (3 x^{8})

Solution

\frac{8 x ^{\frac{5}{3}}}{3}

Solution steps

\frac{d}{d x} (3 x^{8})

Apply the chain rule:

\frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{8})

= \frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \cdot 8 x^{7}

Simplify

\frac{1}{3 ( x ^{8} ) ^{\frac{2}{3}}} \cdot 8 x^{7} : \frac{8 x ^{\frac{5}{3}}}{3}

= \frac{8 x ^{\frac{5}{3}}}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{x^8} ?
The derivative of \sqrt[3]{x^8} is (8x^{5/3})/3
What is the first derivative of \sqrt[3]{x^8} ?
The first derivative of \sqrt[3]{x^8} is (8x^{5/3})/3