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

Lösung

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

2 e^{x^{2}} x + 2 e^{x^{2}} x^{3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

e^{x^{2}} \cdot 2 x x^{2} = 2 e^{x^{2}} x^{3}

= 2 e^{x^{2}} x + 2 e^{x^{2}} x^{3}

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