derivative 3x^{4/3}-2x^{1/7}

解

導関数

3 x^{\frac{4}{3}} - 2 x^{\frac{1}{7}}

\frac{- 2 + 28 x ^{\frac{25}{21}}}{7 x ^{\frac{6}{7}}}

解答ステップ

\frac{d}{d x} (3 x^{\frac{4}{3}} - 2 x^{\frac{1}{7}})

和/差の法則を適用:

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

= \frac{d}{d x} (3 x^{\frac{4}{3}}) - \frac{d}{d x} (2 x^{\frac{1}{7}})

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

\frac{d}{d x} (2 x^{\frac{1}{7}}) = \frac{2}{7 x ^{\frac{6}{7}}}

= 4 x^{\frac{1}{3}} - \frac{2}{7 x ^{\frac{6}{7}}}

簡素化

4 x^{\frac{1}{3}} - \frac{2}{7 x ^{\frac{6}{7}}} : \frac{- 2 + 28 x ^{\frac{25}{21}}}{7 x ^{\frac{6}{7}}}

= \frac{- 2 + 28 x ^{\frac{25}{21}}}{7 x ^{\frac{6}{7}}}