What is the derivative of 1/(\sqrt[8]{x)} ?

The derivative of 1/(\sqrt[8]{x)} is -1/(8x^{9/8)}

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

The first derivative of 1/(\sqrt[8]{x)} is -1/(8x^{9/8)}

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derivative of

- \frac{1}{8 x ^{\frac{9}{8}}}

Solution steps

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

- \frac{1}{8} x^{- \frac{1}{8} - 1} : - \frac{1}{8 x ^{\frac{9}{8}}}

= - \frac{1}{8 x ^{\frac{9}{8}}}

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