(\partial)/(\partial y)((1-xy)^{-2})

解答

\frac{\partial}{\partial y} ((1 - x y)^{- 2})

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

求解步骤

\frac{\partial}{\partial y} ((1 - x y)^{- 2})

将

x

视为常数

使用连锁律:

- \frac{2}{( 1 - x y ) ^{3}} \frac{\partial}{\partial y} (1 - x y)

= - \frac{2}{( 1 - x y ) ^{3}} \frac{\partial}{\partial y} (1 - x y)

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

= - \frac{2}{( 1 - x y ) ^{3}} (- x)

化简

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

= \frac{2 x}{( 1 - x y ) ^{3}}