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Popolare Calcoli >

(\partial)/(\partial x)(2(xe^{x/2+y}+1))

Soluzione

\frac{\partial}{\partial x} (2 (x e^{\frac{x}{2} + y} + 1))

Soluzione

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

Fasi della soluzione

\frac{\partial}{\partial x} (2 (x e^{\frac{x}{2} + y} + 1))

Considera

y

come costante

Elimina la costante:

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

= 2 \frac{\partial}{\partial x} (x e^{\frac{x}{2} + y} + 1)

Applica la regola della somma/differenza:

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

= 2 (\frac{\partial}{\partial x} (x e^{\frac{x}{2} + y}) + \frac{\partial}{\partial x} (1))

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

\frac{\partial}{\partial x} (1) = 0

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

Semplificare

2 (e^{\frac{x}{2} + y} + \frac{e ^{\frac{x + 2 y}{2}} x}{2} + 0) : e^{\frac{x + 2 y}{2}} x + 2 e^{\frac{x}{2} + y}

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

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