derivative x(2x+7)^{2/3}

解

導関数

x (2 x + 7)^{\frac{2}{3}}

\frac{10 x + 21}{3 ( 2 x + 7 ) ^{\frac{1}{3}}}

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (2 x + 7)^{\frac{2}{3}}

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

\frac{d x}{d x} = 1

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

= 1 \cdot (2 x + 7)^{\frac{2}{3}} + \frac{4}{3 ( 2 x + 7 ) ^{\frac{1}{3}}} x

簡素化

1 \cdot (2 x + 7)^{\frac{2}{3}} + \frac{4}{3 ( 2 x + 7 ) ^{\frac{1}{3}}} x : \frac{10 x + 21}{3 ( 2 x + 7 ) ^{\frac{1}{3}}}

= \frac{10 x + 21}{3 ( 2 x + 7 ) ^{\frac{1}{3}}}