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Beliebt Rechnen >

derivative of (16/((1+2x)^3))

Lösung

\frac{d}{d x} (\frac{16}{( 1 + 2 x ) ^{3}})

Lösung

- \frac{96}{( 1 + 2 x ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{16}{( 1 + 2 x ) ^{3}})

Entferne die Konstante:

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

= 16 \frac{d}{d x} (\frac{1}{( 1 + 2 x ) ^{3}})

Wende Exponentenregel an:

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

= 16 \frac{d}{d x} ((1 + 2 x)^{- 3})

Wende die Kettenregel an:

- \frac{3}{( 1 + 2 x ) ^{4}} \frac{d}{d x} (1 + 2 x)

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

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

= 16 (- \frac{3}{( 1 + 2 x ) ^{4}} \cdot 2)

Vereinfache

16 (- \frac{3}{( 1 + 2 x ) ^{4}} \cdot 2) : - \frac{96}{( 1 + 2 x ) ^{4}}

= - \frac{96}{( 1 + 2 x ) ^{4}}

Graph

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