(\partial)/(\partial x)(x(1-x-2y))

解答

\frac{\partial}{\partial x} (x (1 - x - 2 y))

- 2 x - 2 y + 1

求解步骤

\frac{\partial}{\partial x} (x (1 - x - 2 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 = 1 - x - 2 y

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

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

\frac{\partial}{\partial x} (1 - x - 2 y) = - 1

= 1 \cdot (1 - x - 2 y) + (- 1) x

化简

1 \cdot (1 - x - 2 y) + (- 1) x : - 2 x - 2 y + 1

= - 2 x - 2 y + 1

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