d/(dy)((x)(x^2+2x+1))

Lösung

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

3 y^{2} + 4 y + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y, g = y^{2} + 2 y + 1

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

\frac{d y}{d y} = 1

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

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

Vereinfache

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

= 3 y^{2} + 4 y + 1

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