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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (3 x) = 3

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

Simplify

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

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

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