Final Answer
$\frac{1}{3\sqrt[3]{x^{2}}}$
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Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(\sqrt[3]{x}\right)$
Specify the 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
$\frac{1}{3\sqrt[3]{x^{2}}}$
Final Answer
$\frac{1}{3\sqrt[3]{x^{2}}}$