How do you find the derivative of $x^{\frac{1}{3}}$ $x^(1/3)$ ?

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How do you find the derivative of $x^{\frac{1}{3}}$ $x^(1/3)$ ?

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Answer 1 · 2016-02-21T15:25:54

$\frac{1}{3} x^{- \frac{2}{3}}$ $1/3x^(-2/3)$

Explanation:

using the $power rule$ $color(blue)" power rule "$

$\frac{d}{d x} (a x^{n}) = n a x^{n - 1}$ $d/dx(ax^n) = nax^(n-1)$

here a = 1 and $n = \frac{1}{3}$ $n = 1/3$

hence $\frac{d}{d x} (x^{\frac{1}{3}}) = \frac{1}{3} \times 1 x^{\frac{1}{3} - 1} = \frac{1}{3} x^{- \frac{2}{3}}$ $d/dx(x^(1/3)) = 1/3xx1 x^(1/3-1) = 1/3x^(-2/3)$

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How do you find the derivative of $x^{\frac{1}{3}}$ $x^(1/3)$ ?

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