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Beliebt Rechnen >

derivative of (x+1(2x+1)(3x+1))

Lösung

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

Lösung

18 x^{2} + 22 x + 6

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 1, g = (2 x + 1) (3 x + 1)

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

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

\frac{d}{d x} ((2 x + 1) (3 x + 1)) = 12 x + 5

= 1 \cdot (2 x + 1) (3 x + 1) + (12 x + 5) (x + 1)

Vereinfache

1 \cdot (2 x + 1) (3 x + 1) + (12 x + 5) (x + 1) : 18 x^{2} + 22 x + 6

= 18 x^{2} + 22 x + 6

Graph

Beliebte Beispiele

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