(\partial)/(\partial x)((3x-3z)/(2y+3z))

解答

\frac{\partial}{\partial x} (\frac{3 x - 3 z}{2 y + 3 z})

\frac{3}{2 y + 3 z}

求解步骤

\frac{\partial}{\partial x} (\frac{3 x - 3 z}{2 y + 3 z})

将

z, y

视为常数

将常数提出:

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

= \frac{1}{2 y + 3 z} \frac{\partial}{\partial x} (3 x - 3 z)

使用微分加减法定则:

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

= \frac{1}{2 y + 3 z} (\frac{\partial}{\partial x} (3 x) - \frac{\partial}{\partial x} (3 z))

\frac{\partial}{\partial x} (3 x) = 3

\frac{\partial}{\partial x} (3 z) = 0

= \frac{1}{2 y + 3 z} (3 - 0)

化简

\frac{1}{2 y + 3 z} (3 - 0) : \frac{3}{2 y + 3 z}

= \frac{3}{2 y + 3 z}

n = 0 \sum \infty n + 1

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