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Beliebt Rechnen >

derivative of (11/((2x+1)^2))

Lösung

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

Lösung

- \frac{44}{( 2 x + 1 ) ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{2}{( 2 x + 1 ) ^{3}} \frac{d}{d x} (2 x + 1)

= - \frac{2}{( 2 x + 1 ) ^{3}} \frac{d}{d x} (2 x + 1)

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

= 11 (- \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2)

Vereinfache

11 (- \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2) : - \frac{44}{( 2 x + 1 ) ^{3}}

= - \frac{44}{( 2 x + 1 ) ^{3}}

Graph

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