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Derivative of $$$\sqrt[3]{x}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(\sqrt[3]{x}\right)$$$.
Solution
Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = \frac{1}{3}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\sqrt[3]{x}\right)\right)} = {\color{red}\left(\frac{1}{3 x^{\frac{2}{3}}}\right)}$$Thus, $$$\frac{d}{dx} \left(\sqrt[3]{x}\right) = \frac{1}{3 x^{\frac{2}{3}}}$$$.
Answer
$$$\frac{d}{dx} \left(\sqrt[3]{x}\right) = \frac{1}{3 x^{\frac{2}{3}}}$$$A
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