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Popular >

derivative of \sqrt[5]{ln(x})

Solution

Solution

\frac{1}{5 x ln ^{\frac{4}{5}} ( x )}

Solution steps

Apply the chain rule:

\frac{1}{5 ( ln ( x ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (x))

= \frac{1}{5 ( ln ( x ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (x))

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

= \frac{1}{5 ( ln ( x ) ) ^{\frac{4}{5}}} \cdot \frac{1}{x}

Simplify

\frac{1}{5 ln ^{\frac{4}{5}} ( x )} \cdot \frac{1}{x} : \frac{1}{5 x ln ^{\frac{4}{5}} ( x )}

= \frac{1}{5 x ln ^{\frac{4}{5}} ( x )}

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\int - 30 x^{\frac{2}{3}} d x

(dy)/(dx)=((e^{x-y}))/(1+e^x)

\frac{d y}{d x} = \frac{( e ^{x - y} )}{1 + e ^{x}}

integral from 0 to 2 of 30000e^{0.03x}

\int_{0}^{2} 30000 e^{0.03 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[5]{ln(x}) ?
The derivative of \sqrt[5]{ln(x}) is 1/(5xln^{4/5)(x)}
What is the first derivative of \sqrt[5]{ln(x}) ?
The first derivative of \sqrt[5]{ln(x}) is 1/(5xln^{4/5)(x)}