(\partial}{\partial x}(\frac{x+y+z)/3)

解答

\frac{\partial}{\partial x} (\frac{x + y + z}{3})

\frac{1}{3}

十进制

0.33333 \dots

求解步骤

\frac{\partial}{\partial x} (\frac{x + y + z}{3})

将

y, z

视为常数

将常数提出:

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

= \frac{1}{3} \frac{\partial}{\partial x} (x + y + z)

使用微分加减法定则:

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

= \frac{1}{3} (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (z))

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

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

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

= \frac{1}{3} (1 + 0 + 0)

化简

= \frac{1}{3}

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