(\partial)/(\partial x)(xe^{xy})

Lösung

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

e^{x y} + e^{x y} x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x y}

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot e^{x y} + e^{x y} y x

Vereinfache

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

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