What is the derivative of \sqrt[7]{ln(x}) ?

The derivative of \sqrt[7]{ln(x}) is 1/(7xln^{6/7)(x)}

What is the first derivative of \sqrt[7]{ln(x}) ?

The first derivative of \sqrt[7]{ln(x}) is 1/(7xln^{6/7)(x)}

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\frac{d}{d x} (7 ln (x))

\frac{1}{7 x ln ^{\frac{6}{7}} ( x )}

Solution steps

\frac{d}{d x} (7 ln (x))

Apply the chain rule:

\frac{1}{7 ( ln ( x ) ) ^{\frac{6}{7}}} \frac{d}{d x} (ln (x))

= \frac{1}{7 ( ln ( x ) ) ^{\frac{6}{7}}} \frac{d}{d x} (ln (x))

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

= \frac{1}{7 ( ln ( x ) ) ^{\frac{6}{7}}} \cdot \frac{1}{x}

Simplify

\frac{1}{7 ln ^{\frac{6}{7}} ( x )} \cdot \frac{1}{x} : \frac{1}{7 x ln ^{\frac{6}{7}} ( x )}

= \frac{1}{7 x ln ^{\frac{6}{7}} ( x )}

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What is the derivative of \sqrt[7]{ln(x}) ?
The derivative of \sqrt[7]{ln(x}) is 1/(7xln^{6/7)(x)}
What is the first derivative of \sqrt[7]{ln(x}) ?
The first derivative of \sqrt[7]{ln(x}) is 1/(7xln^{6/7)(x)}