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

Lösung

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

\frac{3 e ^{6 x y} x y}{2} + e^{6 x y}

Schritte zur Lösung

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

Vereinfache

x e^{6 x y} : e^{6 x y} x

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{6 x y}, g = x

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

\frac{\partial}{\partial x} (e^{6 x y}) = \frac{3 y e ^{6 y x}}{2 x}

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

= \frac{3 y e ^{6 y x}}{2 x} x + 1 \cdot e^{6 x y}

Vereinfache

\frac{3 y e ^{6 y x}}{2 x} x + 1 \cdot e^{6 x y} : \frac{3 e ^{6 x y} x y}{2} + e^{6 x y}

= \frac{3 e ^{6 x y} x y}{2} + e^{6 x y}

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