What is the derivative of y=x^{-2/3} ?

The derivative of y=x^{-2/3} is -2/(3x^{5/3)}

What is the first derivative of y=x^{-2/3} ?

The first derivative of y=x^{-2/3} is -2/(3x^{5/3)}

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derivative

- \frac{2}{3 x ^{\frac{5}{3}}}

Solution steps

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

Apply the Power Rule:

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

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

Simplify

- \frac{2}{3} x^{- \frac{2}{3} - 1} : - \frac{2}{3 x ^{\frac{5}{3}}}

= - \frac{2}{3 x ^{\frac{5}{3}}}

What is the derivative of y=x^{-2/3} ?
The derivative of y=x^{-2/3} is -2/(3x^{5/3)}
What is the first derivative of y=x^{-2/3} ?
The first derivative of y=x^{-2/3} is -2/(3x^{5/3)}