(\partial)/(\partial z)(xy+yz-xz)

Lösung

\frac{\partial}{\partial z} (x y + yz - x z)

y - x

Schritte zur Lösung

\frac{\partial}{\partial z} (x y + yz - x z)

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial z} (x y) = 0

\frac{\partial}{\partial z} (yz) = y

\frac{\partial}{\partial z} (x z) = x

= 0 + y - x

Vereinfache

= y - x

1 - y^{2} d x = 1 - x^{2} d y

x \to 0 lim (\frac{- 2 e ^{- x}}{2 x - 2})

\int \frac{e ^{4 x}}{- 4 x} d x

x \to + 0 lim (\frac{( 3 e ^{x} - 3 )}{x})

\int_{0}^{1} 0.5 e^{- 2 x} d x