What is the derivative of 2\sqrt[3]{x^4} ?

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

What is the first derivative of 2\sqrt[3]{x^4} ?

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

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\frac{8 x ^{\frac{1}{3}}}{3}

Solution steps

Take the constant out:

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

Apply the chain rule:

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

= \frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

Simplify

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

= \frac{8 x ^{\frac{1}{3}}}{3}

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