derivative 5x^{7/4}+5x^{1/3}-2

解

導関数

5 x^{\frac{7}{4}} + 5 x^{\frac{1}{3}} - 2

\frac{105 x ^{\frac{17}{12}} + 20}{12 x ^{\frac{2}{3}}}

解答ステップ

\frac{d}{d x} (5 x^{\frac{7}{4}} + 5 x^{\frac{1}{3}} - 2)

和/差の法則を適用:

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

= \frac{d}{d x} (5 x^{\frac{7}{4}}) + \frac{d}{d x} (5 x^{\frac{1}{3}}) - \frac{d}{d x} (2)

\frac{d}{d x} (5 x^{\frac{7}{4}}) = \frac{35 x ^{\frac{3}{4}}}{4}

\frac{d}{d x} (5 x^{\frac{1}{3}}) = \frac{5}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (2) = 0

= \frac{35 x ^{\frac{3}{4}}}{4} + \frac{5}{3 x ^{\frac{2}{3}}} - 0

簡素化

\frac{35 x ^{\frac{3}{4}}}{4} + \frac{5}{3 x ^{\frac{2}{3}}} - 0 : \frac{105 x ^{\frac{17}{12}} + 20}{12 x ^{\frac{2}{3}}}

= \frac{105 x ^{\frac{17}{12}} + 20}{12 x ^{\frac{2}{3}}}