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

解

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

\frac{- 32 x ^{\frac{25}{12}} + 9}{6 x ^{\frac{7}{4}}}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (4 x^{\frac{4}{3}}) = \frac{16 x ^{\frac{1}{3}}}{3}

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

\frac{d}{d x} (3) = 0

= - \frac{16 x ^{\frac{1}{3}}}{3} - (- \frac{3}{2 x ^{\frac{7}{4}}}) + 0

簡素化

- \frac{16 x ^{\frac{1}{3}}}{3} - (- \frac{3}{2 x ^{\frac{7}{4}}}) + 0 : \frac{- 32 x ^{\frac{25}{12}} + 9}{6 x ^{\frac{7}{4}}}

= \frac{- 32 x ^{\frac{25}{12}} + 9}{6 x ^{\frac{7}{4}}}