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Beliebt Rechnen >

derivative 2/((6x^2+5x+1)^2)

Lösung

ableitung von

\frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{2}}

Lösung

- \frac{4 ( 12 x + 5 )}{( 6 x ^{2} + 5 x + 1 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{2}})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (\frac{1}{( 6 x ^{2} + 5 x + 1 ) ^{2}})

Wende Exponentenregel an:

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

= 2 \frac{d}{d x} ((6 x^{2} + 5 x + 1)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{3}} \frac{d}{d x} (6 x^{2} + 5 x + 1)

= - \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{3}} \frac{d}{d x} (6 x^{2} + 5 x + 1)

\frac{d}{d x} (6 x^{2} + 5 x + 1) = 12 x + 5

= 2 (- \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{3}} (12 x + 5))

Vereinfache

2 (- \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{3}} (12 x + 5)) : - \frac{4 ( 12 x + 5 )}{( 6 x ^{2} + 5 x + 1 ) ^{3}}

= - \frac{4 ( 12 x + 5 )}{( 6 x ^{2} + 5 x + 1 ) ^{3}}

Graph

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