derivative of 20x^{12/5}-6x^{2/13}

解

\frac{d}{d x} (20 x^{\frac{12}{5}} - 6 x^{\frac{2}{13}})

\frac{- 12 + 624 x ^{\frac{146}{65}}}{13 x ^{\frac{11}{13}}}

解答ステップ

\frac{d}{d x} (20 x^{\frac{12}{5}} - 6 x^{\frac{2}{13}})

和/差の法則を適用:

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

= \frac{d}{d x} (20 x^{\frac{12}{5}}) - \frac{d}{d x} (6 x^{\frac{2}{13}})

\frac{d}{d x} (20 x^{\frac{12}{5}}) = 48 x^{\frac{7}{5}}

\frac{d}{d x} (6 x^{\frac{2}{13}}) = \frac{12}{13 x ^{\frac{11}{13}}}

= 48 x^{\frac{7}{5}} - \frac{12}{13 x ^{\frac{11}{13}}}

簡素化

48 x^{\frac{7}{5}} - \frac{12}{13 x ^{\frac{11}{13}}} : \frac{- 12 + 624 x ^{\frac{146}{65}}}{13 x ^{\frac{11}{13}}}

= \frac{- 12 + 624 x ^{\frac{146}{65}}}{13 x ^{\frac{11}{13}}}