What is the derivative of \sqrt[3]{2x} ?

The derivative of \sqrt[3]{2x} is (2^{1/3})/(3x^{2/3)}

What is the first derivative of \sqrt[3]{2x} ?

The first derivative of \sqrt[3]{2x} is (2^{1/3})/(3x^{2/3)}

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

Solution steps

Apply the chain rule:

\frac{1}{3 ( 2 x ) ^{\frac{2}{3}}} \frac{d}{d x} (2 x)

= \frac{1}{3 ( 2 x ) ^{\frac{2}{3}}} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= \frac{1}{3 ( 2 x ) ^{\frac{2}{3}}} \cdot 2

Simplify

\frac{1}{3 ( 2 x ) ^{\frac{2}{3}}} \cdot 2 : \frac{2 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

= \frac{2 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

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What is the derivative of \sqrt[3]{2x} ?
The derivative of \sqrt[3]{2x} is (2^{1/3})/(3x^{2/3)}
What is the first derivative of \sqrt[3]{2x} ?
The first derivative of \sqrt[3]{2x} is (2^{1/3})/(3x^{2/3)}