derivative 9x^{1/3}+9/2 x^{4/3}

解

導関数

9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}}

\frac{3 + 6 x}{x ^{\frac{2}{3}}}

解答ステップ

\frac{d}{d x} (9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}})

簡素化

9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}} : 9 x^{\frac{1}{3}} + \frac{9 x ^{\frac{4}{3}}}{2}

= \frac{d}{d x} (9 x^{\frac{1}{3}} + \frac{9 x ^{\frac{4}{3}}}{2})

和/差の法則を適用:

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

= \frac{d}{d x} (9 x^{\frac{1}{3}}) + \frac{d}{d x} (\frac{9 x ^{\frac{4}{3}}}{2})

\frac{d}{d x} (9 x^{\frac{1}{3}}) = \frac{3}{x ^{\frac{2}{3}}}

\frac{d}{d x} (\frac{9 x ^{\frac{4}{3}}}{2}) = 6 x^{\frac{1}{3}}

= \frac{3}{x ^{\frac{2}{3}}} + 6 x^{\frac{1}{3}}

簡素化

\frac{3}{x ^{\frac{2}{3}}} + 6 x^{\frac{1}{3}} : \frac{3 + 6 x}{x ^{\frac{2}{3}}}

= \frac{3 + 6 x}{x ^{\frac{2}{3}}}