(\partial)/(\partial x)(x^2e^{5xy})

Lösung

\frac{\partial}{\partial x} (x^{2} e^{5 x y})

2 x e^{5 x y} + e^{5 x y} \cdot 5 y x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} e^{5 x y})

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x^{2}, g = e^{5 x y}

= \frac{\partial}{\partial x} (x^{2}) e^{5 x y} + \frac{\partial}{\partial x} (e^{5 x y}) x^{2}

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

\frac{\partial}{\partial x} (e^{5 x y}) = e^{5 x y} \cdot 5 y

= 2 x e^{5 x y} + e^{5 x y} \cdot 5 y x^{2}

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