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

解答

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

2 (e^{2 y + x^{2}} + 2 e^{2 y + x^{2}} x (x - y))

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

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

= 2 (1 \cdot e^{2 y + x^{2}} + e^{2 y + x^{2}} \cdot 2 x (x - y))

化简

= 2 (e^{2 y + x^{2}} + 2 e^{2 y + x^{2}} x (x - y))

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