What is the derivative of \sqrt[3]{x^2-4} ?

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

What is the first derivative of \sqrt[3]{x^2-4} ?

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

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\frac{2 x}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} - 4)

= \frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} - 4)

\frac{d}{d x} (x^{2} - 4) = 2 x

= \frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \cdot 2 x

Simplify

\frac{1}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}} \cdot 2 x : \frac{2 x}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}}

= \frac{2 x}{3 ( x ^{2} - 4 ) ^{\frac{2}{3}}}

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