derivative of (24/((x-1)^5))

Lösung

\frac{d}{d x} (\frac{24}{( x - 1 ) ^{5}})

- \frac{120}{( x - 1 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{24}{( x - 1 ) ^{5}})

Entferne die Konstante:

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

= 24 \frac{d}{d x} (\frac{1}{( x - 1 ) ^{5}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 24 \frac{d}{d x} ((x - 1)^{- 5})

Wende die Kettenregel an:

- \frac{5}{( x - 1 ) ^{6}} \frac{d}{d x} (x - 1)

= - \frac{5}{( x - 1 ) ^{6}} \frac{d}{d x} (x - 1)

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

= 24 (- \frac{5}{( x - 1 ) ^{6}} \cdot 1)

Vereinfache

24 (- \frac{5}{( x - 1 ) ^{6}} \cdot 1) : - \frac{120}{( x - 1 ) ^{6}}

= - \frac{120}{( x - 1 ) ^{6}}

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