(\partial)/(\partial x)((-9x-7y)/((5x+3y)))

解答

\frac{\partial}{\partial x} (\frac{- 9 x - 7 y}{( 5 x + 3 y )})

\frac{8 y}{( 5 x + 3 y ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{- 9 x - 7 y}{( 5 x + 3 y )})

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} ( - 9 x - 7 y ) ( 5 x + 3 y ) - \frac{\partial}{\partial x} ( 5 x + 3 y ) ( - 9 x - 7 y )}{( 5 x + 3 y ) ^{2}}

\frac{\partial}{\partial x} (- 9 x - 7 y) = - 9

\frac{\partial}{\partial x} (5 x + 3 y) = 5

= \frac{( - 9 ) ( 5 x + 3 y ) - 5 ( - 9 x - 7 y )}{( 5 x + 3 y ) ^{2}}

化简

\frac{( - 9 ) ( 5 x + 3 y ) - 5 ( - 9 x - 7 y )}{( 5 x + 3 y ) ^{2}} : \frac{8 y}{( 5 x + 3 y ) ^{2}}

= \frac{8 y}{( 5 x + 3 y ) ^{2}}