derivative 6(x-3)^{2/3}

解

導関数

6 (x - 3)^{\frac{2}{3}}

\frac{4}{( x - 3 ) ^{\frac{1}{3}}}

解答ステップ

\frac{d}{d x} (6 (x - 3)^{\frac{2}{3}})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} ((x - 3)^{\frac{2}{3}})

連鎖法則を適用:

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

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

\frac{d}{d x} (x - 3) = 1

= 6 \cdot \frac{2}{3 ( x - 3 ) ^{\frac{1}{3}}} \cdot 1

簡素化

6 \cdot \frac{2}{3 ( x - 3 ) ^{\frac{1}{3}}} \cdot 1 : \frac{4}{( x - 3 ) ^{\frac{1}{3}}}

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