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Popular >

derivative of 3\sqrt[3]{x^4}

Solution

Solution

4 x^{\frac{1}{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}

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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