What is the derivative of 1/(\sqrt[7]{x)} ?

The derivative of 1/(\sqrt[7]{x)} is -1/(7x^{8/7)}

What is the first derivative of 1/(\sqrt[7]{x)} ?

The first derivative of 1/(\sqrt[7]{x)} is -1/(7x^{8/7)}

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derivative of

- \frac{1}{7 x ^{\frac{8}{7}}}

Solution steps

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

= - \frac{1}{7} x^{- \frac{1}{7} - 1}

Simplify

- \frac{1}{7} x^{- \frac{1}{7} - 1} : - \frac{1}{7 x ^{\frac{8}{7}}}

= - \frac{1}{7 x ^{\frac{8}{7}}}

(sin (\frac{3}{x}))^{^{'}}

\frac{d}{d x} (\frac{2 x ^{2}}{3})

(1 + x)^{- \frac{3}{5}}

\frac{d}{d x} (17 e^{x^{2}})

What is the derivative of 1/(\sqrt[7]{x)} ?
The derivative of 1/(\sqrt[7]{x)} is -1/(7x^{8/7)}
What is the first derivative of 1/(\sqrt[7]{x)} ?
The first derivative of 1/(\sqrt[7]{x)} is -1/(7x^{8/7)}