(\partial)/(\partial y)(y^2e^{xy})

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

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