(\partial)/(\partial y)(y(2x+y^3))

Lösung

\frac{\partial}{\partial y} (y (2 x + y^{3}))

2 x + 4 y^{3}

Schritte zur Lösung

\frac{\partial}{\partial y} (y (2 x + y^{3}))

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y, g = 2 x + y^{3}

= \frac{\partial}{\partial y} (y) (2 x + y^{3}) + \frac{\partial}{\partial y} (2 x + y^{3}) y

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (2 x + y^{3}) = 3 y^{2}

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

Vereinfache

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

= 2 x + 4 y^{3}

\int 5 - 4 x^{2} d x

\int x + sin (x) d x

\int \frac{x ^{3} + 33}{x ^{2} + 7 x + 12} d x

\int \frac{x + 1}{x ^{2} + 2 x + 7} d x

d er i v a t i v e f (x) = 8 x^{5} - 8