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Beliebt Rechnen >

(\partial)/(\partial x)(y^2+2e^{x^2}xy)

Lösung

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

Lösung

2 y (2 e^{x^{2}} x^{2} + e^{x^{2}})

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= 0 + 2 y (2 e^{x^{2}} x^{2} + e^{x^{2}})

Vereinfache

= 2 y (2 e^{x^{2}} x^{2} + e^{x^{2}})

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integral of (ln(x^2))/2

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(\partial)/(\partial y)(sqrt(29-x^2-4y^2))

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