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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

e x p an d \frac{5 s ^{2} + s + 4}{( s + 4 ) ( s ^{2} + 4 )}

e x p an d (6 - x + 2) (3 - x - 1)

e x p an d \frac{\partial}{\partial x} ((x - y)^{2}) + (y - 2)^{2}

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

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