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Popular >

derivative of \sqrt[3]{1+x^4}

Solution

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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