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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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