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Popular >

derivative of \sqrt[8]{x^9}

Solution

Solution

\frac{9 x ^{\frac{1}{8}}}{8}

Solution steps

Apply the chain rule:

\frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \frac{d}{d x} (x^{9})

= \frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \frac{d}{d x} (x^{9})

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \cdot 9 x^{8}

Simplify

\frac{1}{8 ( x ^{9} ) ^{\frac{7}{8}}} \cdot 9 x^{8} : \frac{9 x ^{\frac{1}{8}}}{8}

= \frac{9 x ^{\frac{1}{8}}}{8}

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[8]{x^9} ?
The derivative of \sqrt[8]{x^9} is (9x^{1/8})/8
What is the first derivative of \sqrt[8]{x^9} ?
The first derivative of \sqrt[8]{x^9} is (9x^{1/8})/8