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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = e^{x^{2} y}

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

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

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

= 1 \cdot e^{x^{2} y} + e^{x^{2} y} \cdot 2 y xx

Vereinfache

1 \cdot e^{x^{2} y} + e^{x^{2} y} \cdot 2 y xx : e^{x^{2} y} + 2 e^{x^{2} y} x^{2} y

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

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