(\partial)/(\partial x)(((3x+8))/(4y+1))

解答

\frac{\partial}{\partial x} (\frac{( 3 x + 8 )}{4 y + 1})

\frac{3}{4 y + 1}

求解步骤

\frac{\partial}{\partial x} (\frac{( 3 x + 8 )}{4 y + 1})

将

y

视为常数

将常数提出:

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

= \frac{1}{4 y + 1} \frac{\partial}{\partial x} (3 x + 8)

使用微分加减法定则:

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

= \frac{1}{4 y + 1} (\frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (8))

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

\frac{\partial}{\partial x} (8) = 0

= \frac{1}{4 y + 1} (3 + 0)

化简

\frac{1}{4 y + 1} (3 + 0) : \frac{3}{4 y + 1}

= \frac{3}{4 y + 1}

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