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Beliebt Rechnen >

derivative (11)/((9x+11)^2)

Lösung

ableitung von

\frac{11}{( 9 x + 11 ) ^{2}}

Lösung

- \frac{198}{( 9 x + 11 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{11}{( 9 x + 11 ) ^{2}})

Entferne die Konstante:

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

= 11 \frac{d}{d x} (\frac{1}{( 9 x + 11 ) ^{2}})

Wende Exponentenregel an:

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

= 11 \frac{d}{d x} ((9 x + 11)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( 9 x + 11 ) ^{3}} \frac{d}{d x} (9 x + 11)

= - \frac{2}{( 9 x + 11 ) ^{3}} \frac{d}{d x} (9 x + 11)

\frac{d}{d x} (9 x + 11) = 9

= 11 (- \frac{2}{( 9 x + 11 ) ^{3}} \cdot 9)

Vereinfache

11 (- \frac{2}{( 9 x + 11 ) ^{3}} \cdot 9) : - \frac{198}{( 9 x + 11 ) ^{3}}

= - \frac{198}{( 9 x + 11 ) ^{3}}

Graph

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