What is the derivative of \sqrt[8]{x} ?

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

What is the first derivative of \sqrt[8]{x} ?

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

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derivative of

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

Solution steps

Apply radical rule:

= \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{7}{8}}}

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

(x^{2} - 9) \frac{d y}{d x} + 6 y = (x + 3)^{2}

x \to 1 + lim (\frac{x - 4}{1 - x})

\frac{\partial}{\partial x} (e^{x - 1})

5 e^{3 t}

\int \frac{x}{x ^{2} + 3} d x

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