(\partial)/(\partial x)(((x+y))/((x-y)^2))

解答

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

\frac{- x - 3 y}{( x - y ) ^{3}}

求解步骤

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

将

y

视为常数

使用微分除法定则:

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

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

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

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

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

化简

\frac{1 \cdot ( x - y ) ^{2} - 2 ( x - y ) ( x + y )}{( ( x - y ) ^{2} ) ^{2}} : \frac{- x - 3 y}{( x - y ) ^{3}}

= \frac{- x - 3 y}{( x - y ) ^{3}}