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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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