(\partial)/(\partial x)((x+y)(xy+1))

Lösung

\frac{\partial}{\partial x} ((x + y) (x y + 1))

y^{2} + 2 x y + 1

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + y) (x y + 1))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x + y, g = x y + 1

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

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

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

= 1 \cdot (x y + 1) + y (x + y)

Vereinfache

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

= y^{2} + 2 x y + 1

\int x^{2} + 6 x + 11 d x

\int sin^{2} (x) sin (3 x) d x

\frac{\partial}{\partial x} (x + 4)

in v erse l a pl a ce \frac{1}{2 s ^{3} + 6 s ^{2} + 4 s}

\int x (x) d x