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

Solution steps

\frac{d}{d x} (\frac{1}{8 x})

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}}}

\frac{d}{d t} (\frac{1}{1 + 4 t ^{2} + 9 t ^{4}})

\frac{d}{d x} ((x + 1)^{x + 1})

\int (3 x + 5) e^{(3 x + 5)} d x

y = 2 e^{x} + \frac{8}{3 x}

\int_{0}^{\frac{π}{2}} cos (\frac{x}{2}) d x

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)}