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Popular >

derivative of \sqrt[3]{x^2+6}

Solution

\frac{d}{d x} (3 x^{2} + 6)

Solution

\frac{2 x}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 x^{2} + 6)

Apply the chain rule:

\frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 6)

= \frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 6)

\frac{d}{d x} (x^{2} + 6) = 2 x

= \frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \cdot 2 x

Simplify

\frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \cdot 2 x : \frac{2 x}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}}

= \frac{2 x}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{x^2+6} ?
The derivative of \sqrt[3]{x^2+6} is (2x)/(3(x^2+6)^{2/3)}
What is the first derivative of \sqrt[3]{x^2+6} ?
The first derivative of \sqrt[3]{x^2+6} is (2x)/(3(x^2+6)^{2/3)}