(\partial)/(\partial x)(6xe^{xy})

Lösung

\frac{\partial}{\partial x} (6 x e^{x y})

6 (e^{x y} + e^{x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (6 x e^{x y})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{\partial}{\partial x} (x e^{x y})

Wende die Produktregel an:

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

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

= 6 (\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

= 6 (1 \cdot e^{x y} + e^{x y} y x)

Vereinfache

= 6 (e^{x y} + e^{x y} x y)

\int sin (x) co x d x

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