derivative of (6x/(2x^{1/3)})

解

\frac{d}{d x} (\frac{6 x}{2 x ^{\frac{1}{3}}})

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

解答ステップ

\frac{d}{d x} (\frac{6 x}{2 x ^{\frac{1}{3}}})

簡素化

\frac{6 x}{2 x ^{\frac{1}{3}}} : 3 x^{\frac{2}{3}}

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

定数を除去:

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

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

乗の法則を適用:

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

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

簡素化

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

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