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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

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

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

Simplify

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

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

Graph

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\int 34 cos (x) cos^{3} (sin (x)) d x

Frequently Asked Questions (FAQ)

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