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Beliebt Rechnen >

(\partial)/(\partial x)(8y-(x+y)^3)

Lösung

\frac{\partial}{\partial x} (8 y - (x + y)^{3})

Lösung

- 3 y^{2} - 6 y x - 3 x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (8 y - (x + y)^{3})

Vereinfache

8 y - (x + y)^{3} : 8 y - x^{3} - 3 y x^{2} - 3 y^{2} x - y^{3}

= \frac{\partial}{\partial x} (8 y - x^{3} - 3 y x^{2} - 3 y^{2} x - y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (8 y) - \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (3 y x^{2}) - \frac{\partial}{\partial x} (3 y^{2} x) - \frac{\partial}{\partial x} (y^{3})

\frac{\partial}{\partial x} (8 y) = 0

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

\frac{\partial}{\partial x} (3 y x^{2}) = 6 y x

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

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

= 0 - 3 x^{2} - 6 y x - 3 y^{2} - 0

Vereinfache

= - 3 y^{2} - 6 y x - 3 x^{2}

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