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Popular >

derivative of \sqrt[3]{9x^2+7}

Solution

Solution

\frac{6 x}{( 9 x ^{2} + 7 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 7)

= \frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 7)

\frac{d}{d x} (9 x^{2} + 7) = 18 x

= \frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \cdot 18 x

Simplify

\frac{1}{3 ( 9 x ^{2} + 7 ) ^{\frac{2}{3}}} \cdot 18 x : \frac{6 x}{( 9 x ^{2} + 7 ) ^{\frac{2}{3}}}

= \frac{6 x}{( 9 x ^{2} + 7 ) ^{\frac{2}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{9x^2+7} ?
The derivative of \sqrt[3]{9x^2+7} is (6x)/((9x^2+7)^{2/3)}
What is the first derivative of \sqrt[3]{9x^2+7} ?
The first derivative of \sqrt[3]{9x^2+7} is (6x)/((9x^2+7)^{2/3)}