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derivative of 3\sqrt[3]{x^2}

Solution

derivative of

Solution

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

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply the chain rule:

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

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

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

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

Simplify

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

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

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x \to 0 lim (\frac{x ^{3}}{x ^{4}})

Frequently Asked Questions (FAQ)

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