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

Lösung

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

x (3 y^{2} + 2 y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

e x p an d [2 + 2] (2 + 1)^{k}

e x p an d \frac{( x ^{2} + 3 x ) ^{2}}{2}

e x p an d - \frac{6 ( s + 1 )}{( s ^{2} + 5 s + 6 )}

e x p an d (2, - 2) y (5, - 3)

e x p an d (- 2 x)^{\circ - 1} (x + y)