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Popular Calculus >

derivative of \sqrt[3]{1+x^2}

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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