derivative of (5x^{1/3})

解答

\frac{d}{d x} ((5 x)^{\frac{1}{3}})

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

求解步骤

\frac{d}{d x} ((5 x)^{\frac{1}{3}})

化简

(5 x)^{\frac{1}{3}} : 5^{\frac{1}{3}} x^{\frac{1}{3}}

= \frac{d}{d x} (5^{\frac{1}{3}} x^{\frac{1}{3}})

将常数提出:

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

= 5^{\frac{1}{3}} \frac{d}{d x} (x^{\frac{1}{3}})

使用幂法则:

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

= 5^{\frac{1}{3}} \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

化简

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

= \frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

\int_{0}^{8} x (\frac{1}{8} x) d x

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