Step-by-step Solution

Find the derivative $\frac{d}{dx}\left(\sqrt[3]{x}\right)$ using the power rule

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$\frac{\frac{1}{3}}{\sqrt[3]{x^{2}}}$

Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(x^{\frac{1}{3}}\right)$

Solving method

1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{1}{3}x^{-\frac{2}{3}}$
2

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{\frac{1}{3}}{\sqrt[3]{x^{2}}}$

$\frac{\frac{1}{3}}{\sqrt[3]{x^{2}}}$
$\frac{d}{dx}\left(x^{\frac{1}{3}}\right)$