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

解答

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

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

求解步骤

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

将常数提出:

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

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

使用幂法则:

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

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

化简

- \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}}}

\int_{- \frac{1}{2}}^{0} x^{4} \cdot e^{2 x + 1} d x

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