(\partial)/(\partial y)(xy-3xz+yz)

Lösung

\frac{\partial}{\partial y} (x y - 3 x z + yz)

x + z

Schritte zur Lösung

\frac{\partial}{\partial y} (x y - 3 x z + yz)

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x y) - \frac{\partial}{\partial y} (3 x z) + \frac{\partial}{\partial y} (yz)

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

\frac{\partial}{\partial y} (3 x z) = 0

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

= x - 0 + z

Vereinfache

= x + z

\int \frac{x ^{5}}{x ^{2} + 8} d x

x \to 3 lim (\frac{- x}{x - 3})

x \to 0 + lim ((tan (2 x))^{x})

\frac{d}{d x} (1 + x^{3})

\frac{d}{d x} (\frac{x ^{2} + x ^{3}}{x ^{2}})