(\partial)/(\partial y)(8xe^{x^2+y^2})

Lösung

\frac{\partial}{\partial y} (8 x e^{x^{2} + y^{2}})

16 e^{x^{2} + y^{2}} x y

Schritte zur Lösung

\frac{\partial}{\partial y} (8 x e^{x^{2} + y^{2}})

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 x \frac{\partial}{\partial y} (e^{x^{2} + y^{2}})

Wende die Kettenregel an:

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

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

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

= 8 x e^{x^{2} + y^{2}} \cdot 2 y

Vereinfache

= 16 e^{x^{2} + y^{2}} x y

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