What is the derivative of \sqrt[3]{6x^2+1} ?

The derivative of \sqrt[3]{6x^2+1} is (4x)/((6x^2+1)^{2/3)}

What is the first derivative of \sqrt[3]{6x^2+1} ?

The first derivative of \sqrt[3]{6x^2+1} is (4x)/((6x^2+1)^{2/3)}

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derivative of

3 6 x^{2} + 1

\frac{4 x}{( 6 x ^{2} + 1 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (6 x^{2} + 1) = 12 x

= \frac{1}{3 ( 6 x ^{2} + 1 ) ^{\frac{2}{3}}} \cdot 12 x

Simplify

\frac{1}{3 ( 6 x ^{2} + 1 ) ^{\frac{2}{3}}} \cdot 12 x : \frac{4 x}{( 6 x ^{2} + 1 ) ^{\frac{2}{3}}}

= \frac{4 x}{( 6 x ^{2} + 1 ) ^{\frac{2}{3}}}

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What is the derivative of \sqrt[3]{6x^2+1} ?
The derivative of \sqrt[3]{6x^2+1} is (4x)/((6x^2+1)^{2/3)}
What is the first derivative of \sqrt[3]{6x^2+1} ?
The first derivative of \sqrt[3]{6x^2+1} is (4x)/((6x^2+1)^{2/3)}