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

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

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

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

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derivative of

y = 8 x

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

Solution steps

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

Apply radical rule:

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

= \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 \to π - lim (csc (x))

\int_{0}^{1} \frac{1}{4 - t ^{2}} d t

y = \frac{5}{x ^{3}}

\frac{d}{d x} ((3 x)^{4 x})

\frac{d}{d x} (c x^{- 7})

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