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Popular >

derivative of \sqrt[9]{ln(x})

Solution

Solution

\frac{1}{9 x ln ^{\frac{8}{9}} ( x )}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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