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Beliebt Rechnen >

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

Lösung

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

Lösung

3 y^{2} + 4 - 4 x

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

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

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

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

Vereinfache

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

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