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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

Graph

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