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Beliebt Rechnen >

(\partial)/(\partial y)(x^3+3x^2y-2y^2)

Lösung

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

Lösung

3 x^{2} - 4 y

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{\partial}{\partial y} (2 y^{2}) = 4 y

= 0 + 3 x^{2} - 4 y

Vereinfache

= 3 x^{2} - 4 y

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