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Popular >

derivative of-2/9 x^{-5/3}

Solution

\frac{d}{d x} (- \frac{2}{9} x^{- \frac{5}{3}})

Solution

\frac{10}{27 x ^{\frac{8}{3}}}

Solution steps

\frac{d}{d x} (- \frac{2}{9} x^{- \frac{5}{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{2}{9} \frac{d}{d x} (x^{- \frac{5}{3}})

Apply the Power Rule:

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

= - \frac{2}{9} (- \frac{5}{3} x^{- \frac{5}{3} - 1})

Simplify

- \frac{2}{9} (- \frac{5}{3} x^{- \frac{5}{3} - 1}) : \frac{10}{27 x ^{\frac{8}{3}}}

= \frac{10}{27 x ^{\frac{8}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of-2/9 x^{-5/3} ?
The derivative of-2/9 x^{-5/3} is (10)/(27x^{8/3)}
What is the first derivative of-2/9 x^{-5/3} ?
The first derivative of-2/9 x^{-5/3} is (10)/(27x^{8/3)}