d/(dy)((x)(6x^3+2x+9))

Lösung

\frac{d}{d y} ((y) (6 y^{3} + 2 y + 9))

24 y^{3} + 4 y + 9

Schritte zur Lösung

\frac{d}{d y} ((y) (6 y^{3} + 2 y + 9))

Wende die Produktregel an:

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

f = y, g = 6 y^{3} + 2 y + 9

= \frac{d y}{d y} (6 y^{3} + 2 y + 9) + \frac{d}{d y} (6 y^{3} + 2 y + 9) y

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

\frac{d}{d y} (6 y^{3} + 2 y + 9) = 18 y^{2} + 2

= 1 \cdot (6 y^{3} + 2 y + 9) + (18 y^{2} + 2) y

Vereinfache

1 \cdot (6 y^{3} + 2 y + 9) + (18 y^{2} + 2) y : 24 y^{3} + 4 y + 9

= 24 y^{3} + 4 y + 9

e x p an d 4 (\frac{32}{π} - \frac{256}{π ^{3}})

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e x p an d \frac{( ( k + 1 ) ^{2} ( ( k + 1 ) + 1 ) ^{2} )}{4}

e x p an d (x^{3} - x + 30)^{7}