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Popular >

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

Solution

derivative of

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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