derivative (11)/((2x^3-5)^4)

Lösung

ableitung von

\frac{11}{( 2 x ^{3} - 5 ) ^{4}}

- \frac{264 x ^{2}}{( 2 x ^{3} - 5 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{11}{( 2 x ^{3} - 5 ) ^{4}})

Entferne die Konstante:

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

= 11 \frac{d}{d x} (\frac{1}{( 2 x ^{3} - 5 ) ^{4}})

Wende Exponentenregel an:

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

= 11 \frac{d}{d x} ((2 x^{3} - 5)^{- 4})

Wende die Kettenregel an:

- \frac{4}{( 2 x ^{3} - 5 ) ^{5}} \frac{d}{d x} (2 x^{3} - 5)

= - \frac{4}{( 2 x ^{3} - 5 ) ^{5}} \frac{d}{d x} (2 x^{3} - 5)

\frac{d}{d x} (2 x^{3} - 5) = 6 x^{2}

= 11 (- \frac{4}{( 2 x ^{3} - 5 ) ^{5}} \cdot 6 x^{2})

Vereinfache

11 (- \frac{4}{( 2 x ^{3} - 5 ) ^{5}} \cdot 6 x^{2}) : - \frac{264 x ^{2}}{( 2 x ^{3} - 5 ) ^{5}}

= - \frac{264 x ^{2}}{( 2 x ^{3} - 5 ) ^{5}}

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