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Popular >

derivative of f(x)=\sqrt[3]{x^4}

Solution

derivative of

Solution

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

Solution steps

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}

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

Simplify

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

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

Popular Examples

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\int \frac{1}{e ^{2 x} + 1} d x

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\int (4 - x) x d x

Frequently Asked Questions (FAQ)

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