What is the derivative of (1-x^{2/3}) ?

The derivative of (1-x^{2/3}) is -2/(3(1-x)^{1/3)}

What is the first derivative of (1-x^{2/3}) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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