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Beliebt Rechnen >

(\partial)/(\partial x)(xy^2z^3+3yz)

Lösung

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

Lösung

y^{2} z^{3}

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

= y^{2} z^{3} + 0

Vereinfache

= y^{2} z^{3}

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