derivative ((8x)^9)/9

解

導関数

\frac{( 8 x ) ^{9}}{9}

134217728 x^{8}

解答ステップ

\frac{d}{d x} (\frac{( 8 x ) ^{9}}{9})

定数を除去:

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

= \frac{1}{9} \frac{d}{d x} ((8 x)^{9})

連鎖法則を適用:

9 (8 x)^{8} \frac{d}{d x} (8 x)

= 9 (8 x)^{8} \frac{d}{d x} (8 x)

\frac{d}{d x} (8 x) = 8

= \frac{1}{9} \cdot 9 (8 x)^{8} \cdot 8

簡素化

\frac{1}{9} \cdot 9 (8 x)^{8} \cdot 8 : 134217728 x^{8}

= 134217728 x^{8}