What is the derivative of \sqrt[3]{8x^2} ?

The derivative of \sqrt[3]{8x^2} is 4/(3x^{1/3)}

What is the first derivative of \sqrt[3]{8x^2} ?

The first derivative of \sqrt[3]{8x^2} is 4/(3x^{1/3)}

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\frac{4}{3 x ^{\frac{1}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 8 x ^{2} ) ^{\frac{2}{3}}} \frac{d}{d x} (8 x^{2})

= \frac{1}{3 ( 8 x ^{2} ) ^{\frac{2}{3}}} \frac{d}{d x} (8 x^{2})

\frac{d}{d x} (8 x^{2}) = 16 x

= \frac{1}{3 ( 8 x ^{2} ) ^{\frac{2}{3}}} \cdot 16 x

Simplify

\frac{1}{3 ( 8 x ^{2} ) ^{\frac{2}{3}}} \cdot 16 x : \frac{4}{3 x ^{\frac{1}{3}}}

= \frac{4}{3 x ^{\frac{1}{3}}}

What is the derivative of \sqrt[3]{8x^2} ?
The derivative of \sqrt[3]{8x^2} is 4/(3x^{1/3)}
What is the first derivative of \sqrt[3]{8x^2} ?
The first derivative of \sqrt[3]{8x^2} is 4/(3x^{1/3)}