What is the derivative of \sqrt[5]{1/x} ?

The derivative of \sqrt[5]{1/x} is -1/(5x^{6/5)}

What is the first derivative of \sqrt[5]{1/x} ?

The first derivative of \sqrt[5]{1/x} is -1/(5x^{6/5)}

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derivative of

5 \frac{1}{x}

- \frac{1}{5 x ^{\frac{6}{5}}}

Solution steps

\frac{d}{d x} (5 \frac{1}{x})

Apply the chain rule:

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

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

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

= \frac{1}{5 ( \frac{1}{x} ) ^{\frac{4}{5}}} (- \frac{1}{x ^{2}})

Simplify

\frac{1}{5 ( \frac{1}{x} ) ^{\frac{4}{5}}} (- \frac{1}{x ^{2}}) : - \frac{1}{5 x ^{\frac{6}{5}}}

= - \frac{1}{5 x ^{\frac{6}{5}}}

\int_{0}^{3.5} 90 x d x

n = 1 \sum \infty \frac{1}{2 n ^{2}}

x^{2} e^{x} - x^{3} - x^{2}

\frac{d}{d t} (2 e^{3 t})

\frac{d}{d x} (\frac{sin ( x )}{7 + cos ( x )})

What is the derivative of \sqrt[5]{1/x} ?
The derivative of \sqrt[5]{1/x} is -1/(5x^{6/5)}
What is the first derivative of \sqrt[5]{1/x} ?
The first derivative of \sqrt[5]{1/x} is -1/(5x^{6/5)}