(\partial)/(\partial x)((5x+8)/(4y+1))

解答

\frac{\partial}{\partial x} (\frac{5 x + 8}{4 y + 1})

\frac{5}{4 y + 1}

求解步骤

\frac{\partial}{\partial x} (\frac{5 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} (5 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} (5 x) + \frac{\partial}{\partial x} (8))

\frac{\partial}{\partial x} (5 x) = 5

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

= \frac{1}{4 y + 1} (5 + 0)

化简

\frac{1}{4 y + 1} (5 + 0) : \frac{5}{4 y + 1}

= \frac{5}{4 y + 1}