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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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