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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

= \frac{1}{3 ( 3 x ^{2} ) ^{\frac{2}{3}}} \cdot 6 x

Simplify

\frac{1}{3 ( 3 x ^{2} ) ^{\frac{2}{3}}} \cdot 6 x : \frac{2}{3 ^{\frac{2}{3}} x ^{\frac{1}{3}}}

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

Graph

Popular Examples

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x^{2} y^{^{'}} - x (x + 2) y = e^{x}

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\int \frac{2 x ^{4} + 7 x ^{3} - x}{x ^{3}} d x

Frequently Asked Questions (FAQ)

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