derivative (9-x/9)^{-7}

解

導関数

(9 - \frac{x}{9})^{- 7}

\frac{33480783}{( 81 - x ) ^{8}}

解答ステップ

\frac{d}{d x} ((9 - \frac{x}{9})^{- 7})

連鎖法則を適用:

- \frac{7}{( 9 - \frac{x}{9} ) ^{8}} \frac{d}{d x} (9 - \frac{x}{9})

= - \frac{7}{( 9 - \frac{x}{9} ) ^{8}} \frac{d}{d x} (9 - \frac{x}{9})

\frac{d}{d x} (9 - \frac{x}{9}) = - \frac{1}{9}

= - \frac{7}{( 9 - \frac{x}{9} ) ^{8}} (- \frac{1}{9})

簡素化

- \frac{7}{( 9 - \frac{x}{9} ) ^{8}} (- \frac{1}{9}) : \frac{33480783}{( 81 - x ) ^{8}}

= \frac{33480783}{( 81 - x ) ^{8}}