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

解

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

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

解答ステップ

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

簡素化

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

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (\frac{3 x ^{\frac{2}{3}}}{8}) = \frac{1}{4 x ^{\frac{1}{3}}}

= x^{\frac{1}{3}} - \frac{1}{4 x ^{\frac{1}{3}}}

簡素化

x^{\frac{1}{3}} - \frac{1}{4 x ^{\frac{1}{3}}} : \frac{- 1 + 4 x ^{\frac{2}{3}}}{4 x ^{\frac{1}{3}}}

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