derivative y=(1-x/7)^{-7}

Lösung

ableitung von

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

\frac{5764801}{( 7 - x ) ^{8}}

Schritte zur Lösung

\frac{d}{d x} ((1 - \frac{x}{7})^{- 7})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (1 - \frac{x}{7}) = - \frac{1}{7}

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

Vereinfache

- \frac{7}{( 1 - \frac{x}{7} ) ^{8}} (- \frac{1}{7}) : \frac{5764801}{( 7 - x ) ^{8}}

= \frac{5764801}{( 7 - x ) ^{8}}

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