derivative of 3/8 (x^{4/3}-2x^{2/3})

解

\frac{d}{d x} (\frac{3}{8} (x^{\frac{4}{3}} - 2 x^{\frac{2}{3}}))

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

解答ステップ

\frac{d}{d x} (\frac{3}{8} (x^{\frac{4}{3}} - 2 x^{\frac{2}{3}}))

定数を除去:

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

= \frac{3}{8} \frac{d}{d x} (x^{\frac{4}{3}} - 2 x^{\frac{2}{3}})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{3}{8} (\frac{d}{d x} (x^{\frac{4}{3}}) - \frac{d}{d x} (2 x^{\frac{2}{3}}))

\frac{d}{d x} (x^{\frac{4}{3}}) = \frac{4 x ^{\frac{1}{3}}}{3}

\frac{d}{d x} (2 x^{\frac{2}{3}}) = \frac{4}{3 x ^{\frac{1}{3}}}

= \frac{3}{8} (\frac{4 x ^{\frac{1}{3}}}{3} - \frac{4}{3 x ^{\frac{1}{3}}})

簡素化

\frac{3}{8} (\frac{4 x ^{\frac{1}{3}}}{3} - \frac{4}{3 x ^{\frac{1}{3}}}) : \frac{x ^{\frac{2}{3}} - 1}{2 x ^{\frac{1}{3}}}

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