(\partial)/(\partial x)((z)(x^2y+4x+3y))

Lösung

\frac{\partial}{\partial x} ((z) (x^{2} y + 4 x + 3 y))

z (2 x y + 4)

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (x^{2} y + 4 x + 3 y))

Behandle

z, y

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial x} (x^{2} y + 4 x + 3 y)

Wende die Summen-/Differenzregel an:

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

= z (\frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (3 y))

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

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

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

= z (2 y x + 4 + 0)

Vereinfache

= z (2 x y + 4)

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