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Beliebt Rechnen >

derivative of 2x(x+1^2)

Lösung

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

Lösung

2 (3 x^{2} + 4 x + 1)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = (x + 1)^{2}

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

\frac{d x}{d x} = 1

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

= 2 (1 \cdot (x + 1)^{2} + 2 (x + 1) x)

Vereinfache

2 (1 \cdot (x + 1)^{2} + 2 (x + 1) x) : 2 (3 x^{2} + 4 x + 1)

= 2 (3 x^{2} + 4 x + 1)

Graph

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