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

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

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

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

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derivative of

\frac{2 r}{3 ( r ^{2} ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d r} (r^{2}) = 2 r

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

Simplify

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

= \frac{2 r}{3 ( r ^{2} ) ^{\frac{2}{3}}}

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