(\partial)/(\partial x)(2xe^{x/2+y}+2)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (2) = 0

= 2 e^{\frac{x}{2} + y} + e^{\frac{x + 2 y}{2}} x + 0

Vereinfache

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

\int \frac{1}{( 6 + x ) ^{3}} d x

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