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Beliebt Rechnen >

(\partial)/(\partial x)(4xy+yz+3xz-32)

Lösung

\frac{\partial}{\partial x} (4 x y + yz + 3 x z - 32)

Lösung

4 y + 3 z

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x y + yz + 3 x z - 32)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (yz) + \frac{\partial}{\partial x} (3 x z) - \frac{\partial}{\partial x} (32)

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

\frac{\partial}{\partial x} (yz) = 0

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

\frac{\partial}{\partial x} (32) = 0

= 4 y + 0 + 3 z - 0

Vereinfache

= 4 y + 3 z

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