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Beliebt Rechnen >

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

Lösung

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

Lösung

4 x - 2 x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 4 x + 0 - 2 y x

Vereinfache

= 4 x - 2 x y

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(\partial)/(\partial x)(sin(1/(x^2+y^2)))

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