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Popular >

derivative of 2\sqrt[3]{x^7}

Solution

Solution

\frac{14 x ^{\frac{4}{3}}}{3}

Solution steps

Take the constant out:

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

Apply the chain rule:

\frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{7})

= \frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

= 2 \cdot \frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \cdot 7 x^{6}

Simplify

2 \cdot \frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \cdot 7 x^{6} : \frac{14 x ^{\frac{4}{3}}}{3}

= \frac{14 x ^{\frac{4}{3}}}{3}

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Frequently Asked Questions (FAQ)

What is the derivative of 2\sqrt[3]{x^7} ?
The derivative of 2\sqrt[3]{x^7} is (14x^{4/3})/3
What is the first derivative of 2\sqrt[3]{x^7} ?
The first derivative of 2\sqrt[3]{x^7} is (14x^{4/3})/3