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Popular >

derivative of (1+x^4)^{2/3}

Solution

derivative of

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

Solution

\frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

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Frequently Asked Questions (FAQ)

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