(\partial)/(\partial x)(xe^{2x+3y})

解答

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

e^{2 x + 3 y} + 2 e^{2 x + 3 y} x

求解步骤

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

将

y

视为常数

使用微分乘法定则:

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

f = x, g = e^{2 x + 3 y}

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

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

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

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

化简

= e^{2 x + 3 y} + 2 e^{2 x + 3 y} x

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