derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4}

解

\frac{d}{d x} (3 x^{\frac{5}{3}} + 4 x^{- \frac{2}{3}} - 7 x^{\frac{3}{4}})

\frac{- 32 - 63 x ^{\frac{17}{12}} + 60 x ^{\frac{7}{3}}}{12 x ^{\frac{5}{3}}}

解答ステップ

\frac{d}{d x} (3 x^{\frac{5}{3}} + 4 x^{- \frac{2}{3}} - 7 x^{\frac{3}{4}})

和/差の法則を適用:

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

= \frac{d}{d x} (3 x^{\frac{5}{3}}) + \frac{d}{d x} (4 x^{- \frac{2}{3}}) - \frac{d}{d x} (7 x^{\frac{3}{4}})

\frac{d}{d x} (3 x^{\frac{5}{3}}) = 5 x^{\frac{2}{3}}

\frac{d}{d x} (4 x^{- \frac{2}{3}}) = - \frac{8}{3 x ^{\frac{5}{3}}}

\frac{d}{d x} (7 x^{\frac{3}{4}}) = \frac{21}{4 x ^{\frac{1}{4}}}

= 5 x^{\frac{2}{3}} - \frac{8}{3 x ^{\frac{5}{3}}} - \frac{21}{4 x ^{\frac{1}{4}}}

簡素化

5 x^{\frac{2}{3}} - \frac{8}{3 x ^{\frac{5}{3}}} - \frac{21}{4 x ^{\frac{1}{4}}} : \frac{- 32 - 63 x ^{\frac{17}{12}} + 60 x ^{\frac{7}{3}}}{12 x ^{\frac{5}{3}}}

= \frac{- 32 - 63 x ^{\frac{17}{12}} + 60 x ^{\frac{7}{3}}}{12 x ^{\frac{5}{3}}}