(\partial)/(\partial y)(y(2-x-y))

Lösung

\frac{\partial}{\partial y} (y (2 - x - y))

2 - x - 2 y

Schritte zur Lösung

\frac{\partial}{\partial y} (y (2 - x - y))

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y, g = 2 - x - y

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

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

\frac{\partial}{\partial y} (2 - x - y) = - 1

= 1 \cdot (2 - x - y) + (- 1) y

Vereinfache

1 \cdot (2 - x - y) + (- 1) y : 2 - x - 2 y

= 2 - x - 2 y

\int x (x^{2} + 1) d x

x y^{^{'}} - y^{^{'}} - (x - 1) sin (x) + y = 0

\int_{0}^{1} (1 + x^{2}) e^{- x} d x

d er i v a t i v e y = \frac{7}{3 - 4 x ^{4}}

(x + 1) y^{^{'}} + (2 x - 1) y = e^{- 2 x}