(\partial)/(\partial x)((12x)/(x+y))

解答

\frac{\partial}{\partial x} (\frac{12 x}{x + y})

\frac{12 y}{( x + y ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{12 x}{x + y})

将

y

视为常数

将常数提出:

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

= 12 \frac{\partial}{\partial x} (\frac{x}{x + y})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 12 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x + y ) - \frac{\partial}{\partial x} ( x + y ) x}{( x + y ) ^{2}}

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

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

= 12 \cdot \frac{1 \cdot ( x + y ) - 1 \cdot x}{( x + y ) ^{2}}

化简

12 \cdot \frac{1 \cdot ( x + y ) - 1 \cdot x}{( x + y ) ^{2}} : \frac{12 y}{( x + y ) ^{2}}

= \frac{12 y}{( x + y ) ^{2}}

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